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%% This program can be redistributed and/or modified under the terms
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% Define the follwing gs-functions if not known, eg when using distiller
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revision 952 gt 
{
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%
/tx@Dict 200 dict def 				% the main PSTricks dictionary
tx@Dict begin
/ADict 25 dict def				% The arrow dictionary
/CM { matrix currentmatrix } bind def
/SLW /setlinewidth load def
/CLW /currentlinewidth load def
/CP /currentpoint load def
/ED { exch def } bind def
/L /lineto load def
/T /translate load def
/TMatrix { } def
/RAngle { 0 } def
/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def  % return 0 for negative arguments 
/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
/ATAN1 {neg -1 atan 180 sub } def		% atan(x) (only one parameter)
/Div { dup 0 eq { pop } { div } ifelse } def  	% control the division
/Log { dup 1e-20 lt { pop -1e30 }{ log } ifelse } def % control the log
/tan { dup cos abs 1.e-10 lt 
  { pop 1.e10 } 				% return 1.e10 as infinit
  { dup sin exch cos div } ifelse 		% default sin/cos
} def
/Tan { dup sin exch cos Div } def 		% sin(x)/cos(x) x in degrees
/Acos {dup dup mul neg 1 add dup 0 lt {		% arc cos, returns 0 when negative root
  pop pop 0 }{ sqrt exch atan} ifelse } def
/Acos2 { 2 dict begin 
  /x ED /y ED
  y abs 1.0e-20 lt { 1.0e30 } if
  x y div 
  dup dup mul neg 1 add dup 0 lt {		% arc cos needs two values x,y
  pop pop 0 }{ sqrt exch atan} ifelse 
  y 0 lt { 180 add } if
} def
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  2 dict begin	% hold all local
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    { b 0 lt 
      { a b cvi exp }
      { a b exp } ifelse 
    }
    { a 0 eq { 0 }{ a b exp } ifelse
    } ifelse
  end
} def
%
/NET { neg exch neg exch T } def	      	% change coordinate system to the negative one		
/Pyth { dup mul exch dup mul add sqrt } def   	% Pythagoras, expects 2 parameter
/addCoors { 
  3 -1 roll 		% xA xB yB yA
  add			% xA xB yB+yA
  3 1 roll 		% yB+yA xA xB
  add			% yB+yA xA+xB
  exch                  % xA+xB yA+yB
} def
/Pyth2 {					% Pythagoras, xA yA xB yB
  3 -1 roll 		% xA xB yB yA
  sub			% xA xB yB-yA
  3 1 roll 		% yB-yA xA xB
  sub			% yB-yA xA-xB
  Pyth } def
/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian (original)
/PtoCrel { pst@angleunit PtoC } def % Polar to Cartesian with \degrees[??]
/PtoCab { dup cos 4 -1 roll mul 3 1 roll sin mul } def % Polar to Cartesian (Ellipse) a b phi-> x y 
/AnytoDeg { pst@angleunit } def 
/DegtoAny { 1 pst@angleunit div} def
/AnytoRad { AnytoDeg DegtoRad } def 
/RadtoAny { RadtoDeg DegtoAny } def
%
%/Rand { rand 4294967295 div } def		% a real random number
/Rand { rand 2147483447 div } def		% a real random number between 0 and 1
%----------------- hv added 20050516 ---------------
/PiDiv2 1.57079632680 def
/Pi 3.14159265359 def 
/TwoPi 6.28318530718 def
/Euler 2.71828182846 def 
%/e Euler bind def
%
/RadtoDeg { 180 mul Pi div } bind def 		% convert from radian to degrees
/DegtoRad { Pi mul 180 div } bind def 		% viceversa
%
/startGlobal { true setglobal globaldict begin } bind def
/endGlobal { end false setglobal } bind def
/pssetRGBcolor /setrgbcolor load def
/pssetCMYKcolor /setcmykcolor load def
/pssetGraycolor /setgray load def
%
%----------------- hv end---------------------------
/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def
%
/PathLength { 
  flattenpath /z 0 def 
  { /y1 ED /x1 ED /y2 y1 def /x2 x1 def }
  { /y ED /x ED PathLength@ } 
  {} 
  { /y y2 def /x x2 def PathLength@ }
  /pathforall load stopped { pop pop pop pop } if 
  z 
} def
%
/STP { .996264 dup scale } def			% BP/PT scaling
/STV { SDict begin normalscale end STP  } def	% 
%
/DashLine {
    dup 0 gt
    { /a .5 def PathLength exch div }
    { pop /a 1 def PathLength } ifelse
    /b ED % pattern should fit evenly in b
    dup /X ED % pattern array
    0 get /y ED % length of first black segment
    /z 0 X {add} forall def % length of the full pattern
    %% Computation of the scaling factor as described by van Zandt:
    b a .5 sub 2 mul y mul sub z Div round
    z mul a .5 sub 2 mul y mul add b exch Div
    %%%% scaling factor on stack.
    /z ED %% now, z is the scaling factor
    false % for the length test below
    X { z mul } forall X astore %% modification TN 04-08-07
    %%% Checking whether at least one dash in X has positive length:
    {0 gt or} forall
    { X 1 a sub y mul }
    { [ 1 0 ] 0 }
    ifelse
    setdash stroke
} def
%
/DotLine { 
  /b PathLength def 
  /a ED /z ED /y CLW def 
  /z y z add def 
  a 0 gt { 
    /b b a div def 
  }{ 
    a 0 eq { 
      /b b y sub def 
    }{ a -3 eq { 
      /b b y add def } if 
    } ifelse 
  } ifelse 
  [ 0 b b z Div round Div dup 0 le { pop 1 } if ] 
  a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse 
  setdash 1 setlinecap stroke 
} def
%
/SymbolLine {   % on stack [ x y x y ...
  counttomark 					% number of elements
  2 div cvi /n ED     				% n pairs
  /YA ED /XA ED					% the start point
  n 1 sub { 
    /YB ED /XB ED
    /XLength XB XA sub def
    /YLength YB YA sub def
    /PAngle YLength XLength Atan def
    /XYLength XLength YLength Pyth def
    %% for negative SymStep we calculate the distance 
    SymStep 0 lt 
      { %XYLength SymStep div abs cvi 
        /nSym SymStep abs cvi def } 
      { /nSym XYLength SymStep div cvi def }
    ifelse
    0.5 setflat
    /Shift Symbol stringwidth pop 2 div def 
    /deltaX XLength nSym div def
    /deltaY YLength nSym div def
    curveticks 
      { XA YA moveto }
      { XA Shift sub YA Shift sub moveto }
    ifelse 
    nSym { 
      gsave 
      curveticks 
        { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED  
          currentpoint translate rotAngle rotate 
          0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
          SymbolLinewidth setlinewidth stroke
        }
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          Symbol show 
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      grestore 
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  curveticks 
    { XA YA moveto }
    { XA Shift sub YA Shift sub moveto }
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  curveticks 
    { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED  
      XA YA translate rotAngle rotate 
      0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
      SymbolLinewidth setlinewidth stroke
    }
    { 
      rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
      Symbol show 
    }
  ifelse 
  grestore
  pop 				% delete the mark symbol
} def
%
/LineFill { % hv ------------ patch 7 -------------
  gsave 
  abs /hatchWidthInc ED
  abs /hatchSepInc ED
  abs CLW add /a ED 
  a 0 dtransform round exch round exch
  2 copy idtransform 
  exch Atan rotate 
  idtransform pop /a ED 
  .25 .25 itransform pathbbox 
  /y2 ED 
  a Div ceiling cvi /x2 ED /y1 ED 
  a Div cvi /x1 ED /y2 y2 y1 sub def 
  clipType   % must be defined in pstricks.tex: clip -- eoclip 
  newpath 
  2 setlinecap 
  systemdict
  /setstrokeadjust known { true setstrokeadjust } if 
  x2 x1 sub 1 add { 
    x1 a mul y1 moveto 0 y2 rlineto stroke 
    /x1 x1 1 add 
      hatchWidthInc 0 gt { CLW add } if 
    def 
    hatchSepInc 0 gt hatchWidthInc 0 gt or { 
      /a a hatchSepInc add def
      CLW hatchWidthInc add SLW 
    } if
  } repeat 
  grestore 
  pop pop } def
%
/DotFill {%	 on stack: dot radius
  /dotRadius ED
  abs CLW add /a ED 
  a 0 dtransform round exch round exch
  2 copy idtransform 
  exch Atan rotate 
  idtransform pop /a ED 
  .25 .25 itransform 
  pathbbox % llx lly urx ury of smallest bounding box
  /y2 ED /x2 ED /y1 ED /x1 ED 
  y2 y1 sub a div 2 add cvi /Ny ED
  x2 x1 sub a div 2 add cvi /Nx ED
  clipType   % must be defined in pstricks.tex: clip -- eoclip 
  newpath 
  /yA y1 dotRadius add CLW add def
  /xA0 x1 dotRadius add CLW add def
  Ny {
     /xA xA0 def
     Nx { 
       newpath 
       xA yA dotRadius 0 360 arc 
       SolidDot { gsave fill grestore } if 
       stroke
       xA a add /xA ED
     } repeat
     yA a add /yA ED
  } repeat
  grestore
} def
%
/PenroseFill {%	 on stack: scaling factor
  /Scale ED
%  1 exch div round /penroseFactor ED 
%  a 0 dtransform round exch round exch
%  2 copy idtransform 
%  exch Atan rotate 
%  idtransform pop /a ED 
%  .25 .25 itransform pathbbox 
%  /y2 ED 
%  a Div ceiling cvi /x2 ED /y1 ED 
%  a Div cvi /x1 ED /y2 y2 y1 sub def 
  clip 
  newpath 
gsave
  220 150 translate
  Scale dup scale
  systemdict /setstrokeadjust known { true setstrokeadjust } if 
  /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
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  [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
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  grestore 
%  pop pop 
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
  /Scale ED
  Scale dup scale
  /border_colour ED 
  /kite_colour ED 
  /dart_colour ED
  clip 
  newpath 
  gsave
  100 100 translate
  6 
  Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
  10					%%%%   Long side length in millimeters
  /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
  /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
  /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
  /l{L f mul}bind def			%%%%   Short side length l = L*f
  /Ll{L l add}bind def			%%%%   Ll =  L + l
  /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
  /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
  /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
	     0 setlinewidth stroke grestore border_colour stroke } bind def
  /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
			   Ll 0 translate 144 rotate kite grestore }
	      		 { kite_colour L draw_tile }ifelse
	     pop } bind def
  /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
			   -144 rotate Ll neg 0 translate half_dart grestore }
	      		 { dart_colour l draw_tile }ifelse
  	     pop } bind def
  /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
  border_width setlinewidth  1 setlinejoin  1 setlinecap
%  450 0 translate  
  dup f exch neg exp dup scale
  5 {kite 72 rotate } repeat stroke 
  grestore
} def
%
%
/TruchetFill { %	 on stack: scaling factor
  10 dict begin
  dup dup scale
  1 exch div round /penroseFactor ED 
  a 0 dtransform round exch round exch
  2 copy idtransform 
  exch Atan rotate 
  idtransform pop /a ED 
  .25 .25 itransform pathbbox 
  /y2 ED 
  a Div ceiling cvi /x2 ED /y1 ED 
  a Div cvi /x1 ED /y2 y2 y1 sub def 
  clip 
  newpath 
  systemdict
  /setstrokeadjust known { true setstrokeadjust } if 
  /ma a neg def
  /ha a 2 div def 
  /mha ha neg def
  /tile { 
    rand dup 2 idiv 2 mul eq { 90 rotate } if
    mha mha moveto ha mha lineto
    ha ha lineto mha ha lineto
%    closepath .1 setlinewidth stroke
    contents
  } def
  /contents{ 
    0 ha moveto ha 0 lineto
    0 mha moveto mha 0 lineto
%    1 setlinewidth stroke
  } def
  /dotiling {
    f ma mul a f a mul { 
      /i exch def
      f ma mul a f a mul { 
        /j exch def
        gsave i j translate
        tile stroke grestore
      } for
    } for
  } def
%
  /f 3 def 
  5 srand dotiling 
  end % local user dict
} def
%
/BeginArrow { 
  ADict begin 			% hold it local, for end see EndArrow
  /@mtrx CM def 
  gsave 
  2 copy T 
  2 index sub neg exch 
  3 index sub exch Atan 
  rotate newpath 
} def
%
/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
%
/Arrow { 
  CLW mul add dup 
  2 div /w ED 
  mul dup /h ED 
  mul /a ED 
  { 0 h T 1 -1 scale } if 
  w neg h moveto 
  0 0 L w h L w neg a neg rlineto 
  gsave fill grestore 
} def
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
  CLW mul add dup 
  2 div /w ED 
  mul dup /h ED 
  mul /Inset ED 
  { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
  w neg h moveto % lower left of >
  w 9 div 4 mul neg h 3 div 2 mul
  w 9 div neg       h 3 div  
  0 0 curveto    % tip of >
  w 9 div        h 3 div  
  w 9 div 4 mul  h 3 div 2 mul
  w h curveto % upper left of >
  w neg Inset neg rlineto % move to x=0 and inset
  gsave fill grestore 
} def 
%
/Tbar { 
  CLW mul add /z ED 
  z -2 div CLW 2 div moveto 
  z 0 rlineto stroke 
  0 CLW moveto 
} def
%
/Bracket { 
  CLW mul add dup CLW sub 2 div 
  /x ED mul CLW add /y ED /z CLW 2 div def 
  x neg y moveto 
  x neg CLW 2 div L x CLW 2 div L x y L stroke 
  0 CLW moveto 
} def
%
/RoundBracket { 
  CLW mul add dup 2 div 
  /x ED mul /y ED /mtrx CM def 
  0 CLW 2 div T x y mul 0 ne { x y scale } if 
  1 1 moveto 
  .85 .5 .35 0 0 0 curveto 
  -.35 0 -.85 .5 -1 1 curveto 
  mtrx setmatrix stroke 0 CLW moveto 
} def
%
/SD { 0 360 arc fill } def
%
/EndDot { % DS is the dot size 
  { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen 
  /b ED 				% the color definition
  0 z DS SD 
  b { 0 z DS CLW sub SD } if 
  0 DS z add CLW 4 div sub 
  moveto 
} def
%
/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
  /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
  load } if ] cvx newpath 3 1 roll T exec } def
%
/NArray { % holds the coordinates and on top of stack the showpoints boolean
  /showpoints ED 
  counttomark 2 div dup cvi /n ED  	% n 2 div on stack 
  n eq not { exch pop } if		% even numbers of points? delete one
  ] aload /Points ED 
  showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} def
%
/Line { 
  NArray n 0 eq not 
    { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def 
      n { Lineto } repeat 
      CP 4 2 roll ArrowB L pop pop 
    } if 
} def
%
/LineToYAxis {
  /Ox ED		% Save the x origin value 
  NArray            % all x-y pairs on stack
  n { 2 copy moveto % go to current point
    Ox exch Lineto   % line to y-axis
    pop             % delete old x-value
  } repeat
} def
%
/LineToXAxis{
  /Oy ED		% Save the y origin value 
  NArray		% all x-y pairs on stack
  n 0 eq not
    { n 1 eq { 0 0 /n 2 def } if
      ArrowA
      /n n 2 sub def
      CP 2 copy moveto pop Oy Lineto
      n { 2 copy moveto pop Oy Lineto } repeat
      CP
      4 2 roll
      ArrowB
      2 copy moveto pop Oy
      L
      pop pop } if
} def
%
/Arcto { 
  /a [ 6 -2 roll ] cvx def 
  a r 
  /arcto load stopped { 5 } { 4 } ifelse { pop } repeat 
  a 
} def
%
/CheckClosed { 
  dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
  and { pop pop /n n 1 sub def } if 
} def
%
/Polygon { 
  NArray n 2 eq { 0 0 /n 3 def } if 
  n 3 lt 
    { n { pop pop } repeat } 
    { n 3 gt { CheckClosed } if 
      n 2 mul -2 roll 
      /y0 ED /x0 ED /y1 ED /x1 ED  
      x1 y1 
      /x1 x0 x1 add 2 div def 
      /y1 y0 y1 add 2 div def 
      x1 y1 moveto 
      /n n 2 sub def 
      n { Lineto } repeat 
      x1 y1 x0 y0 6 4 roll Lineto
      Lineto pop pop closepath } ifelse 
} def
%
/SymbolPolygon {   % on stack [ x y x y ...
  counttomark 					% number of elements
  2 add /m ED
  2 copy m 2 roll				% copy last two
  m 2 div cvi /n ED    				% n pairs
  /YA ED /XA ED					% the start point
  n 1 sub { 
    /YB ED /XB ED
    /XLength XB XA sub def
    /YLength YB YA sub def
    /PAngle YLength XLength Atan def
    /XYLength XLength YLength Pyth def
    /nSym XYLength SymStep Div cvi def
    /Shift Symbol stringwidth pop 2 Div def 
    /deltaX XLength nSym Div def
    /deltaY YLength nSym Div def
    XA Shift sub YA Shift sub moveto 
    nSym { 
      gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
      Symbol show 
      grestore 
      deltaX deltaY rmoveto
    } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
    /YA YB def /XA XB def
  } repeat 
  pop	% delete the mark symbol
} def
%
/Diamond { 
  /mtrx CM def 
  T rotate 
  /h ED 
  /w ED 
  dup 0 eq { pop } { CLW mul neg 
    /d ED 
    /a w h Atan def 
    /h d a sin Div h add def 
    /w d a cos Div w add def } ifelse 
  mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div 
  /ArrowA { moveto } def 
  /ArrowB { } def 
  false Line 
  closepath mtrx setmatrix } def
%
/Triangle { 
  /mtrx CM def 
  translate 
  rotate /h ED 2 div /w ED 
  dup CLW mul /d ED 
  /h h d w h Atan sin Div sub def 
  /w w d h w Atan 2 div dup cos exch sin Div mul sub def 
  mark 
  0 d w neg d 0 h w d 0 d 
  /ArrowA { moveto } def 
  /ArrowB { } def 
  false 
  Line 
  closepath 
  mtrx
% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
% setmatrix } def
  setmatrix pop 
} def
% DG/SR modification end
%
/CCA { 
  /y ED /x ED 
  2 copy y sub /dy1 ED 
  x sub /dx1 ED 
  /l1 dx1 dy1 Pyth def 
} def
%
/CC { 
  /l0 l1 def 
  /x1 x dx sub def 
  /y1 y dy sub def 
  /dx0 dx1 def 
  /dy0 dy1 def 
  CCA 
  /dx dx0 l1 c exp mul dx1 l0 c exp mul add def 
  /dy dy0 l1 c exp mul dy1 l0 c exp mul add def 
  /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def 
  /x2 x l0 dx mul m mul sub def
  /y2 y l0 dy mul m mul sub def 
  /dx l1 dx mul m mul neg def 
  /dy l1 dy mul m mul neg def 
} def
%
/IC { 
  /c c 1 add def 
  c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse 
  /a a 2 mul 3 div 45 cos b exp div def 
  CCA 
  /dx 0 def 
  /dy 0 def 
} def
%
/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
/NC { CC x1 y1 x2 y2 x y curveto } def
/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
/NAC { x2 y2 x y curveto CC x1 y1 } def
/EAC { x2 y2 x y ArrowB curveto pop pop } def
%
/OpenCurve { 
  NArray n 3 lt 
    { n { pop pop } repeat } 
    { BOC /n n 3 sub def n { NC } repeat EOC } ifelse 
} def
%
/CurvePath { 
  %% for negative SymStep we calculate the distance 
  SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
  0.5 setflat
  flattenpath /z 0 def /z0 0 def
  { /y1 ED /x1 ED /y2 y1 def /x2 x1 def 
    x1 Shift sub y1 Shift sub moveto 
    gsave 
    curveticks 
      { x1 y1 translate startAngle rotate 
        0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
        SymbolLinewidth setlinewidth stroke      
      }
      { startAngle rotate Symbol show }
    ifelse 
    grestore /z0 z def }
  { /y ED /x ED PathLength@ z z0 sub SymStep ge {
      x Shift sub y Shift sub moveto 
      gsave 
      curveticks 
        { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED  
          x y translate rotAngle rotate 
          0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
          SymbolLinewidth setlinewidth stroke
        }
        { 
          rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if        
          Symbol show 
        }
      ifelse 
      grestore /z0 z def } if 
    /yOld y def /xOld x def } 
  {} %% the lineto part
  { /y y2 def /x x2 def PathLength@ 
    x Shift sub y Shift sub moveto 
    gsave
    curveticks 
      { y yOld sub x xOld sub Atan 180 sub /rotAngle ED  
        x y translate rotAngle rotate 
        0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
        SymbolLinewidth setlinewidth stroke
      }
      { 
        x Shift sub y Shift sub moveto 
        rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if        
        Symbol show 
      }
    ifelse 
    grestore
  }
  pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
  z 
} def
%
/OpenSymbolCurve { 
  OpenCurve
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/AltCurve { 
  { false NArray n 2 mul 2 roll 
    [ n 2 mul 3 sub 1 roll ] aload
    /Points ED 
    n 2 mul -2 roll } 
  { false NArray } ifelse 
  n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse 
} def
%
/AltOpenSymbolCurve { 
  AltCurve
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/ClosedCurve { 
  NArray n 3 lt 
    { n { pop pop } repeat } 
    { n 3 gt { CheckClosed } if 
      6 copy n 2 mul 6 add 6 roll 
      IC CC x y moveto n { NC } repeat 
      closepath pop pop 
    } ifelse 
} def
%
/ClosedSymbolCurve { 
  ClosedCurve
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
  10 dict begin
  /getX { Points exch 2 mul get } def
  /getY { Points exch 2 mul 1 add get } def
  /n Points length 1 sub 2 idiv def
  /GetFirstControlPoints {
    /x n array def
    /tmp n array def
    /b 2 def
    x 0 rhs 0 get b div put
    1 1 n 1 sub {
      /i exch def
      tmp i 1 b div dup 4 1 roll put
      i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
      x i rhs i get x i 1 sub get sub b div put
    } for
    1 1 n 1 sub {
      n exch sub
      dup dup x exch 1 sub 2 copy 6 2 roll
      get 3 1 roll tmp exch get
      exch x exch get mul sub
      put	
    } for
    x
  } def
  % 
  n 1 eq {
    0 getX 2 mul 1 getX add 3 div
    0 getY 2 mul 1 getY add 3 div
    exch dup 3 1 roll 2 mul 0 getX sub
    exch dup 3 1 roll 2 mul 0 getY sub
    [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
  } {
    /outPoints 6 n mul 2 add array def
    0 1 n {
      dup dup 6 mul dup 1 add
      outPoints exch 5 -1 roll getY put
      outPoints exch 3 -1 roll getX put
    } for
    /rhs n array def
    1 1 n 2 sub {
      rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
    } for
    rhs 0 0 getX 1 getX 2 mul add put
    rhs n 1 sub dup getX 8 mul n getX add 2 div put
    GetFirstControlPoints
    1 1 n 2 sub {
      rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
    } for
    rhs 0 0 getY 1 getY 2 mul add put
    rhs n 1 sub dup getY 8 mul n getY add 2 div put
    GetFirstControlPoints
    0 1 n 1 sub {
      /i exch def
      2 copy
      i get outPoints 6 i mul 3 add 3 -1 roll put
      i get outPoints 6 i mul 2 add 3 -1 roll put
      2 copy
      i n 1 sub lt {
        i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
        i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
      }{
        n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
        n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
      } ifelse
    } for
    pop pop
  } ifelse
  outPoints
  end
} def
/Spline {
  /showpoints ED
  counttomark 2 div dup cvi /n ED
  n eq not { exch pop } if
  ] /Points ED
  n 1 gt {
    CalcBezierSpline
    mark exch aload pop
    ArrowA
    n 2 sub {
      6 2 roll 4 2 roll curveto
    } repeat
    6 2 roll 4 2 roll ArrowB curveto
  } if
} def
/OpenSymbolSpline {
  Spline
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
%
/FontDot { 
  DS 2 mul dup 
  matrix scale matrix concatmatrix exch matrix
  rotate matrix concatmatrix exch 
  findfont exch makefont setfont 
} def
%
/Rect { 
  x1 y1 y2 add 2 div moveto 
%  x1 y2 lineto 
%  x2 y2 lineto 
%  x2 y1 lineto
%  x1 y1 lineto 
  x1 y1 lineto  % counter clockwise path
  x2 y1 lineto 
  x2 y2 lineto
  x1 y2 lineto 
  closepath 
} def
%
/OvalFrame { 
  x1 x2 eq y1 y2 eq or 
    { pop pop x1 y1 moveto x2 y2 L } 
    { y1 y2 sub abs x1 x2 sub abs 2 copy gt 
      { exch pop } { pop } ifelse 
      2 div exch { dup 3 1 roll mul exch } if 
      2 copy lt { pop } { exch pop } ifelse
      /b ED 
      x1 y1 y2 add 2 div moveto 
      x1 y2 x2 y2 b arcto 
      x2 y2 x2 y1 b arcto
      x2 y1 x1 y1 b arcto 
      x1 y1 x1 y2 b arcto 
      16 { pop } repeat 
      closepath 
    } ifelse 
} def
%
/Frame { 
  CLW mul /a ED 
  3 -1 roll 
  2 copy gt { exch } if 
  a sub /y2 ED 
  a add /y1 ED 
  2 copy gt { exch } if 
  a sub /x2 ED 
  a add /x1 ED 
  1 index 0 eq { pop pop Rect } { OvalFrame } ifelse 
} def
%
/BezierNArray { 
  /f ED 
  counttomark 2 div dup cvi /n ED 
  n eq not { exch pop } if 
  n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat 
  f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse 
} def
%
/OpenBezier { 
  BezierNArray 
  n 1 eq 
    { pop pop } 
    { ArrowA n 4 sub 3 idiv 
      { 6 2 roll 4 2 roll curveto } repeat 
      6 2 roll 4 2 roll ArrowB curveto } ifelse 
} def
%
/OpenSymbolBezier { 
  OpenBezier
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/ClosedBezier { 
  BezierNArray 
  n 1 eq 
    { pop pop } 
    { moveto n 1 sub 3 idiv 
      { 6 2 roll 4 2 roll curveto } repeat 
      closepath } ifelse 
} def
%
/ClosedSymbolBezier { 
  /f ED				 % save showpoints value 
  2 copy /yEnd ED /xEnd ED
  counttomark -2 roll 2 copy /yStart ED /xStart ED
  counttomark 2 roll
  f
  ClosedBezier
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
  [ xEnd yEnd xStart yStart SymbolLine 
} def
%
/BezierShowPoints { 
  gsave 
  Points aload length 2 div cvi /n ED 
  moveto 
  n 1 sub { lineto } repeat 
  CLW 2 div SLW [ 4 4 ] 0 setdash stroke 
  grestore 
} def
%
/Parab { 
  /y0 ED /x0 ED /y1 ED /x1 ED 
  /dx x0 x1 sub 3 div def 
  /dy y0 y1 sub 3 div def 
  x0 dx sub y0 dy add x1 y1 ArrowA
  x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB 
  curveto 
  /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def 
} def
%
/Parab1 { % 1 end  |  0 SP
  /ySP ED /xSP ED /y1 ED /x1 ED 
  /dx xSP x1 sub 3 div def 
  /dy ySP y1 sub 3 div def 
  newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto 
                       x1 ySP lineto closepath clip 
  currentpoint
  newpath moveto
  xSP dx sub ySP dy add x1 y1 ArrowA
  xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB 
  curveto 
  /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid { 
  newpath 
  /a 4 string def 
  /b ED % 				psk@gridlabels in pt
  /c ED % 				{ \pst@usecolor\psgridlabelcolor }
  /n ED % 				psk@griddots
  cvi dup 1 lt { pop 1 } if 
  /s ED % 				\psk@subgriddiv
  s div dup 0 eq { pop 1 } if 
  /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
  /dx ED dy div round dy mul         %	\pst@number\psxunit abs
  /y0 ED dx div round dx mul 
  /x0 ED dy div round cvi 
  /y2 ED dx div round cvi 
  /x2 ED dy div round cvi 
  /y1 ED dx div round cvi 
  /x1 ED 
  /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def 
  /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def 
  b 0 gt { 
    /z1 b 4 div CLW 2 div add def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    Helvetica findfont b scalefont setfont 
%    is set in pstricks.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
%     /NimbusSanL-Regu findfont b scalefont setfont   
  /b b .95 mul CLW 2 div add def } if 
  systemdict /setstrokeadjust known 
    { true setstrokeadjust /t { } def }
    { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
       exch itransform } bind def } ifelse 
  gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse 
  /i x1 def 
  /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def 
  /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def 
  x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if 
  dup % run loop two times: lines and labels
  { i dx mul dup xGridOffset add y0 moveto % draw the lines
    dup t f moveto 
    g t L stroke 
    /i i w add def 
  } repeat 
  /i x1 def 
  GridDX div ceiling cvi 
  { i dx mul GridDX mul dup xGridOffset add y0 moveto % plot the labels
    b 0 gt 
      { gsave c i GridDX mul a cvs dup stringwidth pop /z2 ED  
        w 0 gt {z1} {z1 z2 add neg} ifelse 
	h 0 gt {b neg}{z1} ifelse exch GridDX div z2 2 div sub exch 
        rmoveto show grestore } if 
    /i i w add def 
  } repeat 
  grestore 
  gsave 
  n 0 gt
    { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
    { 2 setlinecap } ifelse 
  /i y1 def 
  /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def 
  /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def 
  y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if 
  dup % run loop two times: lines and labels
  { newpath i dy mul dup yGridOffset add x0 exch moveto 
    dup f exch t moveto 
    g exch t L stroke 
    /i i h add def 
  } repeat 
  /i y1 def 
  GridDY div ceiling cvi
  { newpath i dy mul GridDY mul dup yGridOffset add x0 exch moveto 
    b 0 gt { gsave c i GridDY mul a cvs dup stringwidth pop 
      /z2 ED 
      w 0 gt {z1 z2 add neg} {z1} ifelse 
      h 0 gt {z1} {b neg} ifelse GridDY div b 2 div sub
      rmoveto show grestore } if 
    /i i h add def 
  } repeat 
  grestore 
} def
%
/ArcArrow { 
  /d ED /b ED /a ED 
  gsave 
  newpath 0 -1000 moveto clip 
  newpath 
  0 1 0 0 b 
  grestore 
  c mul 
  /e ED 
  pop pop pop r a e d PtoC y add exch x add
  exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
  mul neg d 
} def
%
%
/isbool { type (booleantype) cvn eq } def
%
/Ellipse { 
  dup isbool { /MoveToStart ED }{ /MoveToStart false def }ifelse  % false or true
  /rotAngle ED
  /mtrx CM def 
  T 
  rotAngle rotate
  scale 
  MoveToStart { 0 0 moveto 1 0 rmoveto } if  % move to the start position
  0 0 1 5 3 roll arc 
  mtrx setmatrix 
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let  M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance 
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack:  1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
  /targetLength ED /angle0 ED
  /x0 rx angle0 cos mul def
  /y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength 
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
  targetLength 57.2958 mul
  angle0 sin rx mul dup mul
  angle0 cos ry mul dup mul
  add sqrt div 
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
  dup 90 ge { pop 90 } if 
  angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a 
% better angle (and put it on top of stack)
  30 { dup
% compute distance D between (x0,y0) and M(t)
    dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
    dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
    exch dup cos rx mul x0 sub  exch sin ry mul y0 sub
% stack contains:  y(t)-y0, x(t)-x0, d
    2 index Div targetLength mul y0 add ry Div exch
    2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
    atan exch pop
  } repeat
% we don't look at what happened... in particular, if targetLength is greater 
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that  | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
  /d ED      % is add or sub
  /b ED      % arrow procedure
  /a1 ED     % angle
  gsave
  newpath
  0 -1000 moveto
  clip                  % Set clippath far from arrow.
  newpath
  0 1 0 0 b             % Draw arrow to determine length.
  grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
  a1 exch ArcAdjust   % Angular position of base of arrow.
  /a2 ED
  pop pop pop
  a2 cos rx mul xOrig add % hv 2007-08-29   x->xOrig
  a2 sin ry mul yOrig add % hv 2007-08-29   y->yOrig
  a1 cos rx mul xOrig add % 
  a1 sin ry mul yOrig add % 
% Now arrow tip coor and base coor are on stack.
  b pop pop pop pop       % Draw arrow, and discard coordinates.
  a2 CLW 8 div
% change value of d (test it by looking if  `` 1 1 d '' gives 2 or not )
  1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
  ArcAdjust
% resets original value of d
  1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse  % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/Rot { CP CP translate 3 -1 roll neg rotate NET  } def
%
/RotBegin { 
  tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if 
  /TMatrix [ TMatrix CM ] cvx def 
  /a ED 
  a Rot /RAngle [ RAngle dup a add ] cvx def 
} def
%
/RotEnd { 
  /TMatrix [ TMatrix setmatrix ] cvx def 
  /RAngle [ RAngle pop ] cvx def 
} def
%
/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
%
/Uput {
  /a ED 
  add 2 div /h ED 2 
  div /w ED 
  /s a sin def 
  /c a cos def 
  /b s abs c abs 2 copy gt dup 
    /q ED 
    { pop } { exch pop } ifelse def 
  /w1 c b div w mul def 
  /h1 s b div h mul def 
  q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse 
} def
%
/UUput { 
  5 dict begin
  /z ED 
  abs /y ED 
  /x ED 
  q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse 
    { x x mul y y mul sub z z mul add sqrt z add } 
    { q { x s div } { x c div } ifelse abs 
    } ifelse 
  a PtoC 
  h1 add exch 
  w1 add exch 
  end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 4 2020-06-09 08:32:19Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.07, 2014/08/01
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
%currentdict /Pi known not { /Pi 3.14159265359 def } if
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
/I2P { AlgParser cvx exec } def  % Infix to Postfix
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp  } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%%   { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%%     NextNonBlankChar dup 0 eq { pop exit } if
%%     dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%%     pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%%   AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
  /NotFirst false def
  { NextNonBlankChar pop AnalyzeExpr
    NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
    dup Strlen eq { exit } if NextNonBlankChar
    dup 44 ne 1 index 124 ne and
    { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
    if  pop 1 add } loop
  AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
  AnalyzePreHook AnalyzeTerm IsEndingExpr
  { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
  { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
  ifelse
  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
  AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
  { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
  { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
  ifelse
  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
  AnalyzePreHook 2 copy get dup IsUnaryOp
  { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
  { pop AnalyzeFactor }
  ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
  AnalyzePreHook AnalyzePower IsEndingFactor
  { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
  { { dup 33 eq%% is there a ! DR 09/2011
      { pop 1 add NextNonBlankChar pop EvalFactorial }
      { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
      ifelse
      IsEndingFactor { pop exit } if } loop }
  ifelse  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
  %% depending of first char either a number, or a literal
  2 copy get dup 40 eq%%an open par
  { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
  { AnalyzeLiteral }
  ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
  exch dup 3 -1 roll dup 3 1 roll
  %%read mantissa
  { 1 add  2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
  dup 101 eq exch 69 eq or
  %%% there is a "e" or "E" -> read exponant
  { 1 add 2 copy get dup IsUnaryOp
    { pop 1 add 2 copy get } if
    { IsNumber not { exit } if 1 add 2 copy get } loop }
  if
  dup 4 1 roll
  3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
  NextNonBlankChar 1 index 4 1 roll
  { IsCondOp not { exit } if 1 add  2 copy get } loop
  2 copy 5 -1 roll
  exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
  dup 48 ge exch dup  57 le 3 -1 roll and exch
  dup 65 ge exch dup  90 le 3 -1 roll and 3 -1 roll or exch
  dup 97 ge exch     122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
  exch dup 3 -1 roll dup 3 1 roll
  %%read literal core
  { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
  4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
  2 copy dup Strlen eq
  %% if end of str is reached -> end !
  { pop pop 0 true }
  %% ending chr -> clpar, comma, |, <, >, =, !,
  {get dup  dup  41 eq
       exch dup 124 eq
       exch dup  93 eq
       exch dup  44 eq
       exch dup  30 eq
       exch dup  60 ge exch 62 le and or or or or or}
  ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
    ReadNumber  cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
    exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
  /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
  43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
  /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
  42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
  /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
  pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
  /ExpressionVector ExpressionVector aload length
  /fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
  ReadLiteral
  dup 40 eq%%% there is an open par -> function call
  { pop 2 index
    dup (Sum) eq { EvalSum }
    { dup (IfTE) eq { EvalCond }
      { dup (Derive) eq { pop EvalDerive }
	{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
          /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
	  exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
  { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
    dup 91 eq%%% there is an open bracket -> vector element
    { pop 1 add NextNonBlankChar pop AnalyzeExpr
      /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
    { pop NextNonBlankChar pop }
    ifelse}
  ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
  %% manage the function descripiton
  1 add ReadNumber 3 1 roll NextNonBlankChar
  44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
  1 add NextNonBlankChar pop
  3 -1 roll cvi
  dup 0 eq
  { pop AnalyzeExpr 3 -1 roll pop 1 add }
  { 1 sub 3 1 roll (x)  exch tx@Derive begin DeriveIndexed end 4 -1 roll
    { (x) tx@Derive begin Derive end } repeat
    ExpressionVector exch /ExpressionVector [] def
    AlgToPs aload length
    /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll  /l2 exch def /l1 exch def
    l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
    1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
  pop 1 add NextNonBlankChar pop
  %% read the variable name
  ReadLiteral pop NextNonBlankChar
  44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
  %% read the initial value
  1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
  2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
  %% read the increment value
  1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
  2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
  %% read the limit value
  1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
  2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
  /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
  5 -1 roll 4 add array astore def
  %% keep ExpressionVector for later and create a new one for internal Sum computation
  ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
  1 add NextNonBlankChar pop AnalyzeExpr
  %% add each term
  /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
  /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
  array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
  dup (cos) eq 1 index (sin) eq or exch (tan) eq or
  { /ExpressionVector ExpressionVector aload length 3.1415926 /div cvx 180 /mul cvx 5 -1 roll 4 add
    array astore def
  } if
} def
/EvalCond {%
  pop 1 add AnalyzeCond NextNonBlankChar
  44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
  ExpressionVector 3 1 roll /ExpressionVector [] def
  1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
  NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
  1 add AnalyzeExpr
  NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
  ExpressionVector
  /ExpressionVector 6 -1 roll aload length dup
  6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
  1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
  3 -1 roll
  dup (=) eq  { /eq } {%
  dup (<) eq  { /lt } {%
  dup (>) eq  { /gt } {%
  dup (>=) eq { /ge } {%
  dup (<=) eq { /ge } {%
  dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
  ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
  cvx exch pop
  /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
  3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end   %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {
  10240 string 3 1 roll 0 3 1 roll
  /Variable exch def
  tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
  3 1 roll 10240 string 3 1 roll 0 3 1 roll
  /Variable exch def
  tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
  4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
           2 copy 7 -1 roll dup length 4 1 roll putinterval add
  6 -2 roll pop pop
  2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
  4 -2 roll 4 index (0) eq
  { (0) StrConcat 7 -1 roll pop }
  { 7 -1 roll 45 eq
    { AddSub AddOpPar true } { false } ifelse
    3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
  2 copy pop 0 6 2 roll GetIntervalNewStr
  7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
  7 index dup (0) eq
  { pop true }%% du=0 nothing added
  { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
  ifelse
  5 index dup (0) eq
  { pop { (0) } { 4 -2 roll 2 copy pop 0  6 2 roll GetIntervalNewStr } ifelse }%%dv=0
  { exch
    { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
    { 5 -2 roll 7 index 43 eq%%something yet added
      { AddAdd false } { AddSub AddOpPar true } ifelse }
    ifelse 11 1 roll
    3 -1 roll StrConcat 10 -1 roll { AddClPar } if
    2 copy pop 0 6 2 roll GetIntervalNewStr }
  ifelse
  mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
  4 -2 roll 7 index dup (0) eq
  { pop false }%%du=0
  { (1) eq%%du=1
    { false }
    { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
    3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
    true }%%du!=0
  ifelse
  5 1 roll 5 index (0) eq
  { 5 -1 roll not { (0) StrConcat } if }%%dv=0
  { 5 -1 roll { AddAdd } if
    4 index (1) eq
    { 8 index StrConcat }
    { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
    ifelse
  }%%dv!=0
  ifelse
  2 copy pop 0 6 2 roll GetIntervalNewStr
  mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
  4 -2 roll
  4 index (0) eq%%dv=0 -> u'/v
  { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
  { 7 index dup (0) eq
    { pop }%%du=0
    { (1) eq%%du=1
      { false }
      { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
      3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
    ifelse
      AddSub
      4 index (1) eq
      { 8 index StrConcat }
      { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
      ifelse
    %}%%dv!=0
    2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
    AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
  ifelse
  2 copy pop 0 6 2 roll GetIntervalNewStr
  mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
  4 -2 roll 7 index (0) eq
  {%%if du=0 then (u^v)'=v'ln(u)u^v
    4 index (0) eq
    { (0) StrConcat }%%if dv=0 then (u^v)'=0
    { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
      8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
      AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
  }
  {%%du!=0
    4 index (0) eq
    {%%if dv=0 then (u^v)'=vu'u^(v-1)
      5 index dup IsStrNumber
      { dup (0) eq
        { StrConcat }
        { dup dup (1) eq exch (1.0) eq or
          { StrConcat  }
	  { StrConcat
	    7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
	    { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
            (*\() StrConcat 8 index StrConcat (\)) StrConcat
            5 index  dup dup (2) eq exch (2.0) eq or
	    { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
      { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
        5 index StrConcat (-1\)) StrConcat } ifelse
    }
    {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
      7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
      AddOpPar 5 index StrConcat (\)*\() StrConcat
      8 index StrConcat (\)^\() StrConcat
      5 index StrConcat (-1\)+\() StrConcat
      4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
      8 index StrConcat (\)^\() StrConcat
      5 index StrConcat (\)*ln\() StrConcat
      8 index StrConcat AddClPar
    } ifelse
  } ifelse
  2 copy pop 0 6 2 roll GetIntervalNewStr
  mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
  4 index (0) eq
  { (0) mark 8 -2 roll  cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
  { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
  true exch
  { dup 48 lt exch dup 57 gt 3 -1 roll or
    exch dup 46 ne%%.
    exch dup 43 ne%%+
    exch 45 ne%%-
    and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
  ReadLiteral dup 40 eq%%% there is an open par -> function call
  { pop (EvalFunc_             ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
  { dup 91 eq%%% there is an open bracket -> vector element
    { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
    { pop EvalVariable }
    ifelse }
  ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
  4 2 roll 4 index (1) ne
  { AddOpPar 4 index StrConcat (\)*) StrConcat } if
  (Eval             ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
  2 copy pop 0 6 2 roll GetIntervalNewStr
  mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
  PreCommonFunc
  { (cos\() StrConcat 5 index StrConcat AddClPar } if
  PostCommonFunc } def
/EvalFunc_cos {%
  PreCommonFunc
  { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
  PostCommonFunc } def
/EvalFunc_tan {%
  PreCommonFunc
  {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
  PostCommonFunc } def
/EvalFunc_asin {%
  PreCommonFunc
  { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
  PostCommonFunc } def
/EvalFunc_acos {%
  PreCommonFunc
  { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
  PostCommonFunc } def
/EvalFunc_atg {%
  PreCommonFunc
  { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
  PostCommonFunc } def
/EvalFunc_floor {%
  PreCommonFunc
  {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
  PostCommonFunc } def
/EvalFunc_ln {%
  PreCommonFunc
  {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
  PostCommonFunc } def
/EvalFunc_exp {%
  PreCommonFunc
  {  (exp\() StrConcat 5 index StrConcat AddClPar } if
  PostCommonFunc } def
/EvalFunc_EXP {%
  PreCommonFunc
  {  (EXP\() StrConcat 5 index StrConcat AddClPar } if
  PostCommonFunc } def
/EvalFunc_sqrt {%
  PreCommonFunc
  { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
  PostCommonFunc } def
/EvalFunc_Fact {%
  PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
  PostCommonFunc } def
/EvalFunc_sh {%
  PreCommonFunc
  { (ch\() StrConcat 5 index StrConcat AddClPar } if
  PostCommonFunc } def
/EvalFunc_ch {%
  PreCommonFunc
  { (sh\() StrConcat 5 index StrConcat AddClPar } if
  PostCommonFunc } def
/EvalFunc_th {%
  PreCommonFunc
  {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
  PostCommonFunc } def
/EvalFunc_Argsh {%
  PreCommonFunc
  { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
  PostCommonFunc } def
/EvalFunc_Argch {%
  PreCommonFunc
  { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
  PostCommonFunc } def
/EvalFunc_Argth {%
  PreCommonFunc
  { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
  PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
  1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
  4 2 roll 4 index (0) eq
  { (0) StrConcat false }
  { 4 index (1)  ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
  2 copy pop 0 6 2 roll GetIntervalNewStr
  mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
  1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
  4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
  4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
  2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
  exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
  1 add NextNonBlankChar pop
  %% read the variable name
  ReadLiteral pop 3 -1 roll pop NextNonBlankChar
  44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
  %% read the initial value
  1 add NextNonBlankChar pop ReadNumber pop
  2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
  %% read the increment value
  1 add NextNonBlankChar pop ReadNumber pop
  2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
  %% read the limit value
  1 add NextNonBlankChar pop ReadNumber pop
  2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
  1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
  4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
  4 index StrConcat AddClPar
  2 copy pop 0 6 2 roll GetIntervalNewStr
  mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
  3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
  NextNonBlankChar
  44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
  1 add NextNonBlankChar pop dup 5 1 roll
  AnalyzeExpr NextNonBlankChar
  44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
  1 add NextNonBlankChar pop
  AnalyzeExpr 1 add NextNonBlankChar pop
  4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
  6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
  2 copy pop 0 6 2 roll GetIntervalNewStr
  mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
  dup (cos) eq 1 index (sin) eq or exch (tan) eq or
  { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
    array astore def
  } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
  dup abs 1 gt { EQDFasinrangeerror  } if
  dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
  dup abs 1 gt { EQDFacosrangeerror  } if
  dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro

%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.06, 2017/12/03
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n! 
  dup 0 eq { 1 }{ 
    dup 1 gt { dup 1 sub factorial mul } if }
  ifelse } def 
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
  2 dict begin
  /n exch def /m exch def
  n 0 eq { 1 }{
    m n eq { 1 }{
      m factorial n factorial m n sub factorial mul div } ifelse } ifelse 
  end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
  5 dict begin       % all local
  aload length /n ED % number of coors
  n 2 div cvi /m ED  % number of Points
  /n1 n def
  m { n1 2 roll /n1 n1 2 sub def } repeat
  n array astore
  end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b] 
% which is a+bi = Real+i Imag
%
/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
  dup 0 get		% [a1 b1] [a2 b2] a2
  3 -1 roll		% [a2 b2] a2 [a1 b1]
  dup 0 get		% [a2 b2] a2 [a1 b1] a1
  3 -1 roll		% [a2 b2] [a1 b1] a1 a2
  add			% [a2 b2] [a1 b1] a1+a2
  3 1 roll		% a1+a2 [a2 b2] [a1 b1]
  1 get			% a1+a2 [a2 b2] b1
  exch 1 get		% a1+a2 b1 b2
  add 2 array astore
} def
%
/cxneg {		% [a b]
  dup 1 get		% [a b] b
  exch 0 get		% b a
  neg exch neg		% -a -b
  2 array astore
} def
%
/cxsub { cxneg cxadd } def  % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul {		% [a1 b1] [a2 b2]
  dup 0 get		% [a1 b1] [a2 b2] a2
  exch 1 get		% [a1 b1] a2 b2
  3 -1 roll		% a2 b2 [a1 b1]
  dup 0 get		% a2 b2 [a1 b1] a1
  exch 1 get		% a2 b2 a1 b1
  dup			% a2 b2 a1 b1 b1
  5 -1 roll dup		% b2 a1 b1 b1 a2 a2
  3 1 roll mul		% b2 a1 b1 a2 b1a2
  5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
  3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
  3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
  4 -1 roll add		% b1 a2 a1 b2 b3
  4 2 roll mul		% b1 b2 b3 a1a2
  4 2 roll mul sub	% b3 a3
  exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr {		% [a b]   square root
  dup 0 get exch 1 get	% a b
  dup dup mul		% a b b^2
  3 -1 roll		% b b^2 a
  dup dup mul 		% b b^2 a a^2
  3 -1 roll sub		% b a a2
  3 1 roll mul 2 mul	% a2 b2	
  2 array astore
} def
%
/cxsqrt {		% [a b]
%  dup cxnorm sqrt /r exch def
%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2 
  cxlog 		% log[a b]
  2 cxrdiv 		% log[a b]/2
  aload pop exch	% b a
  2.781 exch exp	% b exp(a)
  exch cxconv exch	% [Re +iIm] exp(a)
  cxrmul		%
} def
%
/cxarg { 		% [a b] 
  aload pop 		% a b
  exch atan 		% arctan b/a
  DegtoRad 		% arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog {		% [a b]
  dup 			% [a b][a b]
  cxnorm 		% [a b] |z|
  log 			% [a b] log|z|
  exch 			% log|z|[a b]
  cxarg 		% log|z| Theta
  cxmake2 		% [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 {		% [a b]
  dup 0 get exch 1 get	% a b
  dup mul			% a b^2
  exch dup mul add	% a^2+b^2
} def
%
/cxnorm {		% [a b]
  cxnorm2 sqrt
} def
%
/cxconj {		% conjugent complex
  dup 0 get exch 1 get	% a b
  neg 2 array astore	% [a -b]
} def
%
/cxre { 0 get } def	% real value
/cxim { 1 get } def	% imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip {		% [a b]
  dup cxnorm2 exch	% n2 [a b]
  dup 0 get exch 1 get	% n2 a b
  3 -1 roll		% a b n2
  dup			% a b n2 n2
  4 -1 roll exch div	% b n2 a/n2
  3 1 roll div		% a/n2 b/n2
  neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def	  % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul {		% [a b] r
  exch aload pop	% r a b
  3 -1 roll dup		% a b r r
  3 1 roll mul		% a r b*r
  3 1 roll mul		% b*r a*r
  exch 2 array astore   % [a*r b*r]
} def
%
% division by a real number
/cxrdiv {		% [a b] r
  1 exch div		% [a b] 1/r
  cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv {		% theta
  RadtoDeg dup sin exch cos cxmake2
} def

%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
   /a exch def
   /n a length 1 sub def
   n 0 gt {
      % at this point only the n+1 items in the bottom of a remain to
      % the sorted largest item in that blocks is to be moved up into
      % position n
      n {
         0 1 n 1 sub {
            /i exch def
            a i get a i 1 add get gt {
               % if a[i] > a[i+1] swap a[i] and a[i+1]
               a i 1 add
               a i get
               a i a i 1 add get
               % set new a[i] = old a[i+1]
               put
               % set new a[i+1] = old a[i]
               put
            } if
         } for
         /n n 1 sub def
      } repeat
   } if
   a % return the sorted array
end
} def
%
/concatstringarray{  %  [(a) (b) ... (z)] --> (ab...z)  20100422
  0 1 index { length add } forall 
  string     
  0 3 2 roll      
  { 3 copy putinterval length add }forall 
  pop  
} bind def
%
/concatstrings{ % (a) (b) -> (ab)  
  1 dict begin
  exch dup length    
  2 index length add string    
  dup dup 4 2 roll copy length
  4 -1 roll putinterval
  end
} def
%
/reversestring { % (aBC) -> (CBa)
  5 dict begin
  /str exch def
  /L str length def
  /strTemp L string def
  /i 0 def
  L { 
    /I L 1 sub i sub def
    strTemp i str I 1 getinterval putinterval
    /i i 1 add def
  } repeat
  strTemp
  end
} def
%
/concatarray{ % [a c] [b d] -> [a c b d]  
  2 dict begin
  /a2 exch def
  /a1 exch def
  [ a1 aload pop a2 aload pop ]
  end
} def
%
/dot2comma {% on stack a string (...) 
  2 dict begin
  /Output exch def
  0 1 Output length 1 sub { 
    /Index exch def 
    Output Index get 46 eq { Output Index 44 put } if 
  } for
  Output
  end
} def
%
/rightTrim { % on stack the string and the character number to be stripped  
  /charNo exch def
  dup
  length 1 sub -1 0 { 
    /i exch def dup i get charNo ne { exit } if 
  } for
  0 i 1 add getinterval
  dup length string copy
} bind def  % leaves the stripped string on the stack

/psStringwidth /stringwidth load def
/psShow /show load def

%/stringwidth{ 32 rightTrim psStringwidth } bind def

%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%

/pgffunctions {
    /pgfsc{}bind def% stroke color is empty by default
    /pgffc{}bind def% fill color is empty by default
    /pgfstr{stroke}bind def%
    /pgffill{fill}bind def%
    /pgfeofill{eofill}bind def%
    /pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
    /pgfw{setlinewidth}bind def% setlinewidth
    /pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale 
      magscale{1 DVImag div dup scale}if 
      pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
    /pgfr{pgfsd restore}bind def %restore
    userdict begin%
    /pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
    /pgfc{newpath @endspecial pgfpd}bind def %close
    /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
    /pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
    /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha 
    /.pgfsetfillopacityalpha{/pgffoa exch def
      /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
      /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
    /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
    /pgffoa 1 def
    /pgfsoa 1 def
    end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 4 2020-06-09 08:32:19Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
  /FontType 3 def
  /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
  /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
  /Encoding 256 array def
  0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
  Encoding				   % replace with given dot names
    dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding 
    dup (c) 0 get /Circle put
    dup (C) 0 get /BoldCircle put	% 67
    dup (u) 0 get /SolidTriangle put
    dup (t) 0 get /Triangle put
    dup (T) 0 get /BoldTriangle put
    dup (r) 0 get /SolidSquare put
    dup (s) 0 get /Square put
    dup (S) 0 get /BoldSquare put
    dup (q) 0 get /SolidPentagon put
    dup (p) 0 get /Pentagon put
    dup (P) 0 get /BoldPentagon put
%%%		  
    dup (k) 0 get /Asterisk put
    dup (K) 0 get /BoldAsterisk put
    dup (J) 0 get /SolidAsterisk put
    dup (h) 0 get /Hexagon put
    dup (H) 0 get /BoldHexagon put
    dup (G) 0 get /SolidHexagon put
    dup (f) 0 get /Octogon put		% 2008-04-18 hv
    dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
    dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
    dup (a) 0 get /Add put
    dup (A) 0 get /BoldAdd put 		% 65
    dup (x) 0 get /Mul put
    dup (X) 0 get /BoldMul put
    dup (m) 0 get /Oplus put
    dup (M) 0 get /BOplus put
    dup (e) 0 get /SolidOplus put
    dup (n) 0 get /Otimes put
    dup (N) 0 get /BOtimes put
    dup (E) 0 get /SolidOtimes put
    dup (i) 0 get /Bar put
    dup (I) 0 get /BoldBar put
    dup (l) 0 get /SolidDiamond put
    dup (d) 0 get /Diamond put
        (D) 0 get /BoldDiamond put
%%%  
/CharProcs 47 dict def
CharProcs begin
  /CirclePath {0 0 500 0 360 arc closepath} def
  /Bullet {CirclePath fill} def
  /Circle {CirclePath .9 .9 scale CirclePath eofill} def
  /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
  /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
  /SolidTriangle {TrianglePath fill} def
  /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
  /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
  /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
  /SolidSquare {SquarePath fill} def
  /Square {SquarePath .89 .89 scale SquarePath eofill} def
  /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
  /PentagonPath {
    -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
    0 574.7 lineto -546.6 177.6 lineto closepath
  } def
  /SolidPentagon {PentagonPath fill} def
  /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
  /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
%-------------- hv begin 2004/07/25   from: er 2003/03/24
  /HexagonPath {
    0 550 moveto -476 275 lineto -476 -275 lineto
    0 -550 lineto 476 -275 lineto 476 275 lineto closepath
  } def
  /SolidHexagon {HexagonPath fill} def
  /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
  /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
  /OctogonPath { 
     550 dup 22.5 tan mul dup neg dup add /xMove exch def 
     exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def 
  /SolidOctogon { OctogonPath fill                             } def
  /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
  /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
  /AsteriskPath {
    20 0 moveto 10 250 180 500 0 500 curveto
    -180 500 -10 250 -20 0 curveto closepath
  } def
  /Asterisk {
    AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
    60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
  } def
%
  /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
  /BoldAsteriskPath {
    50 30 cos 100 mul moveto  Basterp
    60 rotate Basterp 60 rotate Basterp
    60 rotate Basterp 60 rotate Basterp
    60 rotate Basterp closepath
  } def
  /BoldAsterisk {BoldAsteriskPath fill} def
  /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
  /CrossPath {
    40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
    -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto 
    40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
  } def
  /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
    -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto 
    80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
  } def
  /Add {CrossPath fill} def
  /Mul {45 rotate CrossPath fill} def
  /BoldAdd {BoldCrossPath fill} def
  /BoldMul {45 rotate BoldCrossPath fill} def
  /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def 
  /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def 
  /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def 
  /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def 
  /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def 
  /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def 
  /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
  /Bar {BarPath fill} def
  /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
  /BoldBar {BoldBarPath fill} def
  /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
  /SolidDiamond {DiamondPath fill} def
  /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
  /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
  /.notdef { } def
end
%
/BuildGlyph {
  exch
  begin 		
%  Metrics 1 index get exec 0
    0 0
%      BBoxes 3 index get exec
    -1000 -1000 1000 1000
%     -571.5 -742.5 571.5 742.5
    setcachedevice
    CharProcs begin load exec end
  end
} def
%
/BuildChar {
  1 index /Encoding get exch get
  1 index /BuildGlyph get exec
} bind def
%
end
/PSTricksDotFont exch definefont pop
%
%% end

%%EndProcSet
%%BeginProcSet: pst-grad.pro 0 0
%!
% PostScript prologue for pst-grad.tex.
% Version 1.05, 2006/11/04 
% prepared by Herbert Voss
% For copying restrictions, see pstricks.tex.
%
% For the PSTricks gradient fillstyle.%
% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).%
% Syntax:% D.G. modification begin - Apr.  9, %1998
%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill
%   ifGradientCircle GradientScale %GradientPosX GradientPosY
%     R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill
% D.G. modification end
%
/tx@GradientDict 40 dict def
tx@GradientDict begin
/GradientFill {
 /ifCMYK exch def   % do we have rgb or cmyk? hv 1.06
 rotate
 /MidPoint ED
 /NumLines ED
 ifCMYK {
    /LastBlack ED	% 1.06
    /LastYellow ED	% 1.06
    /LastMagenta ED	% 1.06
    /LastCyan ED	% 1.06
    /FirstBlack ED	% 1.06
    /FirstYellow ED	% 1.06
    /FirstMagenta ED	% 1.06
    /FirstCyan ED	% 1.06
 }{ /LastBlue ED
    /LastGreen ED
    /LastRed ED
    /FirstBlue ED
    /FirstGreen ED
    /FirstRed ED
 } ifelse
 /GradientPosY ED
 /GradientPosX ED
 /GradientScale ED
 /ifGradientCircle ED
 % This avoids gaps due to rounding errors:
 clip
 pathbbox           %leave llx,lly,urx,ury on stack
 4 copy /ury ED /urx ED /lly ED /llx ED
 /y ED /x ED
 ifGradientCircle
   { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if }
   {2 copy translate} ifelse
 y sub neg /y ED
 x sub neg /x ED  % This avoids gaps due to rounding errors:
 ifCMYK {				% 1.06
    LastCyan FirstCyan add 2 div	% 1.06
    LastMagenta FirstMagenta add 2 div	% 1.06
    LastYellow FirstYellow add 2 div	% 1.06
    LastBlack FirstBlack add 2 div	% 1.06
    setcmykcolor			% 1.06
  }{
    LastRed FirstRed add 2 div
    LastGreen FirstGreen add 2 div
    LastBlue FirstBlue add 2 div
    setrgbcolor
  } ifelse
 ifGradientCircle
   { /YSizePerLine y NumLines div def
     /CurrentY y 2 div def
     /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def
   }{
     fill
     /YSizePerLine y NumLines div def
     /CurrentY 0 def
     /MidLine NumLines 1 MidPoint sub mul abs cvi def
   } ifelse
 MidLine NumLines 2 sub gt 
   { /MidLine NumLines def }
   { MidLine 2 lt { /MidLine 0 def } if } ifelse
 MidLine 0 gt {
  ifCMYK {
    /Cyan FirstCyan def
    /Magenta FirstMagenta def
    /Yellow FirstYellow def
    /Black FirstBlack def
    /CyanIncrement LastCyan FirstCyan sub MidLine 1 sub div def
    /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def
    /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def
    /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def
  }{
    /Red FirstRed def
    /Green FirstGreen def
    /Blue FirstBlue def
    /RedIncrement LastRed FirstRed sub MidLine 1 sub div def
    /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def
    /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def
  } ifelse
  MidLine { GradientLoop } repeat
 } if
 MidLine NumLines lt {
  ifCMYK {
    /Cyan LastCyan def
    /Magenta LastMagenta def
    /Yellow LastYellow def
    /Black LastBlack def
    /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def
    /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def
    /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def
    /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def
  }{
    /Red LastRed def
    /Green LastGreen def
    /Blue LastBlue def
    /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def
    /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def
    /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def
  } ifelse
  NumLines MidLine sub { GradientLoop } repeat  
 } if
} def/GradientLoop {
% D.G. modification begin - Jul. 23, 1997 / Apr.  9, 1998
  ifGradientCircle
   {CurrentY 0 gt {
% The default center used is the center of the bounding box of the object
      0 GradientPosX eq        {0 GradientPosX eq
           {/GradientPosX urx llx sub 2 div def
            /GradientPosY ury lly sub 2 div def} if} if
      GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc
      ifCMYK { Cyan Magenta Yellow Black setcmykcolor }
           { Red Green Blue setrgbcolor } ifelse 
      fill
      /CurrentY CurrentY YSizePerLine sub def
      ifCMYK {
        /Cyan Cyan CyanIncrement add def
        /Magenta Magenta MagentaIncrement add def
        /Yellow Yellow YellowIncrement add def
        /Black Black BlackIncrement add def
      }{	
        /Blue Blue BlueIncrement add def
        /Green Green GreenIncrement add def
        /Red Red RedIncrement add def
      } ifelse
  } if }   { 0 CurrentY moveto    x 0 rlineto
    0 YSizePerLine rlineto    x neg 0 rlineto    closepath
      ifCMYK { Cyan Magenta Yellow Black setcmykcolor }
           { Red Green Blue setrgbcolor } ifelse 
      fill    
      /CurrentY CurrentY YSizePerLine add def
      ifCMYK {
        /Cyan Cyan CyanIncrement add def
        /Magenta Magenta MagentaIncrement add def
        /Yellow Yellow YellowIncrement add def
        /Black Black BlackIncrement add def
      }{	
        /Blue Blue BlueIncrement add def
        /Green Green GreenIncrement add def
        /Red Red RedIncrement add def
      } ifelse
      } ifelse% D.G. modification end
    }def
%
/GradientFillHSB { %	hv 2006-11-04
  rotate
  /MidPoint ED
  /NumLines ED
  /LastBrightness ED
  /LastSaturation ED
  /LastHue ED
  /FirstBrightness ED
  /FirstSaturation ED
  /FirstHue ED
  % This avoids gaps due to rounding errors:
  clip
  pathbbox           %leave llx,lly,urx,ury on stack
  /y ED /x ED
  2 copy translate
  y sub neg /y ED
  x sub neg /x ED
  % This avoids gaps due to rounding errors:
  LastHue FirstHue add 2 div
  LastSaturation FirstSaturation add 2 div
  LastBrightness FirstBrightness add 2 div
  sethsbcolor
  fill
  /YSizePerLine y NumLines div def
  /CurrentY 0 def
  /MidLine NumLines 1 MidPoint sub mul abs cvi def
  MidLine NumLines 2 sub gt
  { /MidLine NumLines def }
  { MidLine 2 lt { /MidLine 0 def } if }
  ifelse
  MidLine 0 gt
  {
    /Hue FirstHue def
    /Saturation FirstSaturation def
    /Brightness FirstBrightness def
    /HueIncrement LastHue FirstHue sub MidLine 1 sub div def
    /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub
                         div def
    /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub
                         div def
    MidLine { GradientLoopHSB } repeat
  } if
  MidLine NumLines lt
  {
    /Hue LastHue def
    /Saturation LastSaturation def
    /Brightness LastBrightness def
    /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def
    /SaturationIncrement FirstSaturation LastSaturation sub
                         NumLines MidLine sub 1 sub div def
    /BrightnessIncrement FirstBrightness LastBrightness sub
                         NumLines MidLine sub 1 sub div def
    NumLines MidLine sub { GradientLoopHSB } repeat
  } if
} def
/GradientLoopHSB {
  0 CurrentY moveto
  x 0 rlineto
  0 YSizePerLine rlineto
  x neg 0 rlineto
  closepath
  Hue Saturation Brightness sethsbcolor fill
  /CurrentY CurrentY YSizePerLine add def
  /Brightness Brightness BrightnessIncrement add def
  /Saturation Saturation SaturationIncrement add def
  /Hue Hue HueIncrement add def
} def
%
end
%
% END pst-grad.pro

%%EndProcSet
%%BeginProcSet: pst-node.pro 0 0
% $Id: pst-node.pro 395 2017-03-21 09:24:38Z herbert $
%%
%% PostScript prologue for pst-node.tex.
%% Version 1.15, 2014/01/27.
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%%%%  EMPTY lines are not alowed!!! Problem with pst-eps -> \par
%
%
tx@Dict begin 			% from main pstricks dict
 /T /translate load def 
 /CP /currentpoint load def 
% /startGlobal { true setglobal globaldict begin } bind def
% /endGlobal { end false setglobal } bind def
end
/tx@NodeDict 400 dict def tx@NodeDict begin
/NewNode { % on stack: { x y } boolean N@name type InitXnode 
  gsave 
  NodeScale                     % a bugfix for xelatex, it's empty for dvips
  /next exch def 		% { x y } boolean N@name type  
  dict dup 			% { x y } boolean N@name dict dict
  3 1 roll def 			% { x y } boolean dict N@name dict def
  exch { dup 3 1 roll def } if  % { x y } dict boolean
  begin 			% { x y } dict begin
  tx@Dict begin 
    STV CP T exec 		% set scaling
  end 
  /NodeMtrx CM def 		% save CM
  next 				% InitXNode
  end
  grestore 
} def
%
/InitPnode { 
  /Y ED /X ED 
  /NodePos { NodeSep Cos mul NodeSep Sin mul } def
} def
%
/InitCnode { 
  /r ED /Y ED /X ED 
  /NodePos { NodeSep r add dup Cos mul exch Sin mul } def 
} def
%
/GetRnodePos { 
  Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse 
  Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse 
  dx Sin mul abs dy 
  Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse 
} def
%
/InitRnode { 
  /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED 
  /NodePos { GetRnodePos } def 
} def
%
/DiaNodePos { 
  w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
  Cos mul exch Sin mul 
} def
%
/TriNodePos { 
  Sin s lt 
    { d NodeSep sub dup Cos mul Sin Div exch } 
    { w h mul w Sin mul h Cos abs mul add Div 
      NodeSep add dup Cos mul exch Sin mul 
    } ifelse 
} def
%
/InitTriNode { 
  sub 2 div exch 
  2 div exch 
  2 copy T 
  2 copy 4 index index /d ED 
  pop pop pop pop 
  -90 mul rotate 
  /NodeMtrx CM def 
  /X 0 def /Y 0 def 
  d sub abs neg /d ED 
  d add /h ED 
  2 div h mul h d sub Div /w ED 
  /s d w Atan sin def 
  /NodePos { TriNodePos } def 
} def
%
/OvalNodePos { 
  /ww w NodeSep add def 
  /hh h NodeSep add def 
  Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul 
} def
%
/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
%
/XYPos { 
  dup sin exch cos Do 
  /Cos ED /Sin ED /Dist ED 
  Cos 0 gt 
    { Dist Dist Sin mul Cos div }
    { Cos 0 lt 
      { Dist neg Dist Sin mul Cos div neg }
      { 0 Dist Sin mul } ifelse 
    } ifelse 
  Do 
} def
%
/GetEdge {
  dup 0 eq 
    { pop begin 1 0 NodeMtrx dtransform 
      CM idtransform 
      exch atan sub 
      dup 
      sin /Sin ED 
      cos /Cos ED 
      /NodeSep ED 
      NodePos NodeMtrx dtransform CM idtransform end }
    { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse 
} def
%
/AddOffset { 
  1 index 0 eq 
    { pop pop } 
    { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse 
} def
%
/GetEdgeA { 
  NodeSepA AngleA NodeA NodeSepTypeA GetEdge 
  OffsetA AngleA AddOffset 
  yA add /yA1 ED 
  xA add /xA1 ED 
} def
%
/GetEdgeB { 
  NodeSepB AngleB NodeB NodeSepTypeB GetEdge 
  OffsetB AngleB AddOffset 
  yB add /yB1 ED 
  xB add /xB1 ED 
} def
%
/GetArmA { 
  ArmTypeA 0 eq 
    { /xA2 ArmA AngleA cos mul xA1 add def 
      /yA2 ArmA AngleA sin mul yA1 add def } 
    { ArmTypeA 1 eq {{exch}} {{}} ifelse 
      /Do ED 
      ArmA AngleA XYPos OffsetA AngleA AddOffset 
      yA add /yA2 ED 
      xA add /xA2 ED } ifelse 
} def
%
/GetArmB { 
  ArmTypeB 0 eq 
    { /xB2 ArmB AngleB cos mul xB1 add def 
      /yB2 ArmB AngleB sin mul yB1 add def } 
    { ArmTypeB 1 eq {{exch}} {{}} ifelse 
      /Do ED
      ArmB AngleB XYPos OffsetB AngleB AddOffset 
      yB add /yB2 ED 
      xB add /xB2 ED } ifelse 
} def
%
/InitNC { 
  /b ED /a ED % second and first node
  /NodeSepTypeB ED /NodeSepTypeA ED 
  /NodeSepB ED /NodeSepA ED 
  /OffsetB ED /OffsetA ED 
  tx@NodeDict a known tx@NodeDict b known and dup { 
    /NodeA a load def 
    /NodeB b load def 
    NodeA GetCenter /yA ED /xA ED 
    NodeB GetCenter /yB ED /xB ED } if 
} def
%
/LPutLine { 
  4 copy 
  3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 
  1 t sub mul 
  3 1 roll 1 t sub mul 
  4 1 roll t mul add /Y ED 
  t mul add /X ED 
} def
%
/LPutLines { 
  mark LPutVar counttomark 2 div 1 sub /n ED 
%  t floor dup n gt 
  t floor dup n ge 		% to allow npos<= hv 2008-08-14
  { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse 
  cvi 2 mul { pop } repeat 
  LPutLine 
  cleartomark 
} def
%
/BezierMidpoint { 
  /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED 
  /cx x1 x0 sub 3 mul def 
  /cy y1 y0 sub 3 mul def 
  /bx x2 x1 sub 3 mul cx sub def 
  /by y2 y1 sub 3 mul cy sub def 
  /ax x3 x0 sub cx sub bx sub def 
  /ay y3 y0 sub cy sub by sub def 
  ax t 3 exp mul bx t t mul mul add 
  cx t mul add x0 add ay t 3 exp mul 
  by t t mul mul add cy t mul add
  y0 add 3 ay t t mul mul mul 2 
  by t mul mul add cy add 3 ax t t mul mul mul 
  2 bx t mul mul add cx add atan /NAngle ED 
  /Y ED /X ED 
} def
%
/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
} def
%
/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
           /NAngle yyB yyA sub xxB xxA sub Atan def 
} def
/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd  } def
%
/HPutLines { HPosBegin yB yA ge 
  { /check { le } def } { /check { ge } def } ifelse 
  /xxA xA def 
  /yyA yA def 
  mark xB yB LPutVar 
    { dup Y check { exit } { /yyA ED /xxA ED } ifelse } 
  loop 
  /yyB ED /xxB ED cleartomark HPosEnd 
} def
%
/VPosBegin { 
  xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
} def
%
/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
/NAngle yyB yyA sub xxB xxA sub Atan def } def
/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd  } def
/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
VPosEnd  } def
/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
def grestore exec /LPutVar /SaveLPutVar load def 
} def
%
/NCCoor { 
  /AngleA yB yA sub xB xA sub Atan def 
  /AngleB AngleA 180 add def
  GetEdgeA GetEdgeB 
  /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def 
  /LPutPos { LPutVar LPutLine } def 
  /HPutPos { LPutVar HPutLine } def 
  /VPutPos { LPutVar VPutLine } def 
  LPutVar 
} def
%
/NCLine { 
  NCCoor 
  tx@Dict begin 
  ArrowA CP 4 2 roll 
  ArrowB 
  lineto pop pop
  end 
} def
%
/NCLines { 
  false NArray 
  n 0 eq 
    { NCLine } 
    { 2 copy yA sub exch xA sub Atan /AngleA ED 
      n 2 mul dup index exch index yB sub exch xB sub 
      Atan /AngleB ED 
      GetEdgeA GetEdgeB 
      /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def 
      mark LPutVar 
      tx@Dict begin false Line end 
      /LPutPos { LPutLines } def 
      /HPutPos { HPutLines } def 
      /VPutPos { VPutLines } def 
    } ifelse 
} def
%
/NCCurve { 
  GetEdgeA 
  GetEdgeB 
  xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
%
/NCAngles { 
  GetEdgeA GetEdgeB GetArmA GetArmB 
  /mtrx AngleA matrix rotate def 
  xA2 yA2 mtrx transform pop 
  xB2 yB2 mtrx transform exch pop 
  mtrx itransform 
  /y0 ED /x0 ED 
  mark ArmB 0 ne { xB1 yB1 } if 
  xB2 yB2 x0 y0 xA2 yA2 
  ArmA 0 ne { xA1 yA1 } if 
  tx@Dict begin false Line end 
  /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def 
  /LPutPos { LPutLines } def
  /HPutPos { HPutLines } def 
  /VPutPos { VPutLines } def } def
%
/NCAngle { 
  GetEdgeA GetEdgeB GetArmB 
  /mtrx AngleA matrix rotate def 
  xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
  /y0 ED /x0 ED 
  mark 
  ArmB 0 ne { xB1 yB1 } if 
  xB2 yB2 x0 y0 xA1 yA1
  tx@Dict begin false Line end 
  /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def 
  /LPutPos { LPutLines } def 
  /HPutPos { HPutLines } def 
  /VPutPos { VPutLines } def 
} def
%
/NCBar { 
  GetEdgeA GetEdgeB GetArmA GetArmB 
  /mtrx AngleA matrix rotate def
  xA2 yA2 mtrx itransform pop 
  xB2 yB2 mtrx itransform pop 
  sub dup 0 mtrx transform 
  3 -1 roll 0 gt 
    { /yB2 exch yB2 add def /xB2 exch xB2 add def }
    { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse 
  mark 
  ArmB 0 ne { xB1 yB1 } if 
  xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if 
  tx@Dict begin false Line end 
  /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def 
  /LPutPos { LPutLines } def 
  /HPutPos { HPutLines } def 
  /VPutPos { VPutLines } def 
} def
%
/NCDiag { 
  /lineAngle ED
  GetEdgeA GetEdgeB GetArmA GetArmB mark
  lineAngle abs 0 gt {
    /xTemp xA2 10 add def
    /yTemp yA2 lineAngle dup sin exch cos div 10 mul add def
    /dY1 yTemp yA2 sub def
    /dX1 xTemp xA2 sub def
    /dY2 yB2 yB1 sub def
    /dX2 xB2 xB1 sub def
    dX1 abs 0.01 lt {
      /m2 dY2 dX2 div def
      /xB2 xA2 def
      /yB2 xA2 xB1 sub m2 mul yB1 add def
    }{
      dX2 abs 0.01 lt {
        /m1 dY1 dX1 div def
        /xB2 xB1 def
        /yB2 xB1 xA2 sub m1 mul yA2 add def
      }{%
        /m1 dY1 dX1 div def
        /m2 dY2 dX2 div def
        /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
        /yB2 xB2 xA2 sub m1 mul yA2 add def
      } ifelse
    } ifelse
  } if
  ArmB 0 ne { xB1 yB1 } if
  xB2 yB2 xA2 yA2 
  ArmA 0 ne { xA1 yA1 } if 
  tx@Dict begin false Line end
  /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def 
  /LPutPos { LPutLines } def 
  /HPutPos { HPutLines } def 
  /VPutPos { VPutLines } def 
%
%  GetEdgeA GetEdgeB GetArmA GetArmB mark 
%  ArmB 0 ne { xB1 yB1 } if
%  xB2 yB2 xA2 yA2 
%  ArmA 0 ne { xA1 yA1 } if 
%  tx@Dict begin false Line end
%  /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def 
%  /LPutPos { LPutLines } def 
%  /HPutPos { HPutLines } def 
%  /VPutPos { VPutLines } def 
} def
%
/NCDiagg { 
  /lineAngle ED
  GetEdgeA GetArmA 
  lineAngle abs 0 gt 
    { lineAngle }
    { yB yA2 sub xB xA2 sub Atan 180 add } ifelse 
  /AngleB ED
  GetEdgeB mark
  lineAngle abs 0 gt {
    /dY2 yA2 yA1 sub def
    /dX2 xA2 xA1 sub def
    lineAngle abs 90 eq {
      /m2 dY2 dX2 div def
      /yA2 xB xA2 sub m2 mul yA2 add def
      /xA2 xB def
    }{
      /m1 lineAngle dup sin exch cos div def % tan alpha
      dX2 abs 0.01 lt {
        /yA2 xA1 xB sub m1 mul yB add def
        /xA2 xA1 def
      }{%
        /m2 dY2 dX2 div def
        /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
        /yA2 xA2 xB sub m1 mul yB add def
      } ifelse
    } ifelse
  } if
  xB1 yB1 xA2 yA2
  ArmA 0 ne { xA1 yA1 } if
  tx@Dict begin false Line end
  /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
  /LPutPos { LPutLines } def
  /HPutPos { HPutLines } def
  /VPutPos { VPutLines } def
%
%  GetEdgeA GetArmA 
%  yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
%  GetEdgeB 
%  mark 
%  xB1 yB1 xA2 yA2 
%  ArmA 0 ne { xA1 yA1 } if 
%  tx@Dict begin false Line end 
%  /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def 
%  /LPutPos { LPutLines } def 
%  /HPutPos { HPutLines } def 
%  /VPutPos { VPutLines } def 
} def
%
/NCLoop { 
  GetEdgeA GetEdgeB GetArmA GetArmB 
  /mtrx AngleA matrix rotate def 
  xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED 
  /xB3 xB2 yB2 mtrx transform pop def 
  xB3 yA3 mtrx itransform /yB3 ED /xB3 ED 
  xA3 yA3 mtrx itransform /yA3 ED /xA3 ED 
  mark ArmB 0 ne { xB1 yB1 } if 
  xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if 
  tx@Dict begin false Line end 
  /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def 
  /LPutPos { LPutLines } def 
  /HPutPos { HPutLines } def 
  /VPutPos { VPutLines } def 
} def
%
% DG/SR modification begin - May 9, 1997 - Patch 1
%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
%
/NCCircle { 
  NodeSepA 0 NodeA 0 GetEdge pop 
  2 div dup 2 exp r r mul sub abs sqrt 
  atan 2 mul /a ED 
  r AngleA 90 add PtoC yA add exch xA add 
  exch 2 copy 
  /LPutVar [ 4 2 roll r AngleA ] cvx def 
  /LPutPos { 
    LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC 
    3 -1 roll add 
    /Y ED add /X ED /NAngle ED
% DG/SR modification end
  } def 
  /HPutPos { LPutPos } def 
  /VPutPos { LPutPos } def 
  r AngleA 90 sub a add AngleA 270 add a sub 
  tx@Dict begin 
  /angleB ED /angleA ED /r ED 
  /c 57.2957 r Div def 
  /y ED /x ED 
} def
%
/NCBox { 
  /d ED /h ED 
  /AngleB yB yA sub xB xA sub Atan def 
  /AngleA AngleB 180 add def 
  GetEdgeA GetEdgeB 
  /dx d AngleB sin mul def 
  /dy d AngleB cos mul neg def 
  /hx h AngleB sin mul neg def 
  /hy h AngleB cos mul def 
  /LPutVar [ 
    xA1 hx add yA1 hy add xB1 hx add yB1 hy add 
    xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def 
  /LPutPos { LPutLines } def 
  /HPutPos { xB yB xA yA LPutLine } def 
  /VPutPos { HPutPos } def 
  mark 
  LPutVar tx@Dict begin false Polygon end 
} def
%
/NCArcBox { 
  /l ED neg /d ED /h ED /a ED 
  /AngleA yB yA sub xB xA sub Atan def 
  /AngleB AngleA 180 add def 
  /tA AngleA a sub 90 add def 
  /tB tA a 2 mul add def 
  /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
  /x0 xA r tA cos mul add def 
  /y0 yA r tA sin mul add def 
  /c 57.2958 r div def 
  /AngleA AngleA a sub 180 add def 
  /AngleB AngleB a add 180 add def
  GetEdgeA GetEdgeB 
  /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def 
  /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def 
  l 0 eq { 
    x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn 
  }{ 
    x0 y0 translate 
    /tA AngleA l c mul add def 
    /tB AngleB l c mul sub def
    0 0 r h add tA tB arc r h add 
    AngleB PtoC r d add 
    AngleB PtoC 2 copy 
    6 2 roll l arcto 4 { pop } repeat 
    r d add tB PtoC l arcto 4 { pop } repeat 
    0 0 r d add tB tA arcn r d add 
    AngleA PtoC r h add 
    AngleA PtoC 2 copy 6 2 roll 
    l arcto 4 { pop } repeat 
    r h add tA PtoC l arcto 4 { pop } repeat 
  } ifelse 
  closepath 
  /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def 
  /LPutPos { 
    LPutVar /d ED /h ED 
    /AngleB ED /AngleA ED 
    /r ED /y0 ED /x0 ED 
    t 1 le { 
      r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC 
    }{t 2 lt { 
        /NAngle AngleB 180 add def r 2 t sub 
        h mul t 1 sub d mul add add AngleB PtoC 
      }{ 
        t 3 lt { 
          r d add AngleB 3 t sub mul AngleA 2 t sub
          mul add dup 90 sub /NAngle ED PtoC 
        }{ 
          /NAngle AngleA 180 add def 
          r 4 t sub d mul t 3 sub h mul add add AngleA PtoC 
        } ifelse 
      } ifelse 
    } ifelse
    y0 add /Y ED x0 add /X ED 
  } def 
  /HPutPos { LPutPos } def 
  /VPutPos { LPutPos } def 
} def
%
/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
%
/LPutCoor { 
  NAngle 
  tx@Dict begin /NAngle ED end 
  gsave 
  CM STV 
  CP Y sub neg exch X sub neg exch moveto 
  setmatrix CP 
  grestore 
} def
%
/LPut { 
  tx@NodeDict /LPutPos known 
    { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse 
  LPutCoor  
} def
%
/HPutAdjust { 
  Sin Cos mul 0 eq 
    { 0 } 
    { d Cos mul Sin div flag not { neg } if 
      h Cos mul Sin div flag { neg } if 
      2 copy gt { pop } { exch pop } ifelse 
    } ifelse 
  s add flag { r add neg }{ l add } ifelse 
  X add /X ED 
} def
%
/VPutAdjust { 
  Sin Cos mul 
  0 eq 
    { 0 }
    { l Sin mul Cos div flag { neg } if
      r Sin mul Cos div flag not { neg } if 
      2 copy gt { pop } { exch pop } ifelse 
    } ifelse 
  s add flag { d add } { h add neg } ifelse 
  Y add /Y ED 
} def
%
%
end
%
% END pst-node.pro

%%EndProcSet
%%BeginProcSet: pst-3d.pro 0 0
%% $Id: pst-3d.pro 247 2010-01-04 22:45:42Z herbert $
% PostScript prologue for pst-3d.tex.
% Version 0.01, 2010/01/01 
%
/tx@3Ddict 300 dict def 
tx@3Ddict begin
%
/SetMatrixThreeD {
  dup sin /e ED cos /f ED
  /p3 ED /p2 ED /p1 ED
  p1 0 eq
  { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def
    p3 p2 abs
  }
  { p2 0 eq
    { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def
      p3 p1 abs
    }
    { p1 dup mul p2 dup mul add sqrt dup
      p1 exch div /a ED
      p2 exch div neg /b ED
      p3 p1 a div
    }
    ifelse
  }
  ifelse
  atan dup sin /c ED cos /d ED
  /Matrix3D
  [
    b f mul c a mul e mul sub
    a f mul c b mul e mul add
    d e mul
    b e mul neg c a mul f mul sub
    a e mul neg c b mul f mul add
    d f mul
  ] def
} def
%
/ProjThreeD {
  /z ED /y ED /x ED
  Matrix3D aload pop
  z mul exch y mul add exch x mul add
  4 1 roll
  z mul exch y mul add exch x mul add
  exch
} def
%
/SetMatrixEmbed {
  SetMatrixThreeD
  Matrix3D aload pop
  /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED
  SetMatrixThreeD
  [
  Matrix3D aload pop
  z3 mul exch z2 mul add exch z1 mul add 4 1 roll
  z3 mul exch z2 mul add exch z1 mul add
  Matrix3D aload pop
  x3 mul exch x2 mul add exch x1 mul add 4 1 roll
  x3 mul exch x2 mul add exch x1 mul add
  3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy
  x3 mul exch x2 mul add exch x1 mul add 4 1 roll
  z3 mul exch z2 mul add exch z1 mul add
  ]
  concat
} def
%
/TMSave {
  tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if 
  /TMatrix [ TMatrix CM ] cvx def 
} def
%
/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
%
/TMChange {
  TMSave
  /cp [ currentpoint ] cvx def % ??? Check this later.
  CM
  CP T STV
  CM matrix invertmatrix    % Inv(M')
  matrix concatmatrix       % M Inv(M')
  exch exec
  concat cp moveto
} def
%
end % of tx@3Ddict
%%
%% End of file `pst-3d.pro'.

%%EndProcSet
%%BeginProcSet: pst-math.pro 0 0
%                           -*- Mode: Postscript -*-
% pst-math.pro --- PostScript header file pst-math.pro
%
% Author          : Christophe JORSSEN 
% Author          : Herbert Voß <hvoss@tug.org>
% Last Mod        : $Date: 2018/12/16 $
% Version         : 0.65 $
%
/PI 3.14159265359 def
/ENeperian 2.71828182846 def
%
/DegToRad {PI mul 180 div} bind def
/RadToDeg {180 mul PI div} bind def
%
/COS {RadToDeg cos} bind def
/SIN {RadToDeg sin} bind def
/TAN {dup SIN exch COS Div} bind def
/tan {dup sin exch cos Div} bind def
/ATAN {neg -1 atan 180 sub DegToRad} bind def
/ACOS {dup dup mul neg 1 add sqrt exch atan DegToRad} bind def
/acos {dup dup mul neg 1 add sqrt exch atan} bind def
/ASEC {1 exch Div ACOS} bind def
/ASIN {neg dup dup mul neg 1 add sqrt neg atan 180 sub DegToRad} bind def
/asin {neg dup dup mul neg 1 add sqrt neg atan 180 sub} bind def
/ACSC {1 exch Div ASIN} bind def
%
/EXP {ENeperian exch exp} bind def
%
/COSH {dup EXP exch neg EXP add 2 div} bind def
/SINH {dup EXP exch neg EXP sub 2 div} bind def
/TANH {dup SINH exch COSH div} bind def
/ACOSH {dup dup mul 1 sub sqrt add ln} bind def
/ASINH {dup dup mul 1 add sqrt add ln} bind def
/ATANH {dup 1 add exch neg 1 add Div ln 2 div} bind def
%
%/SINC {dup SIN exch Div} bind def
/SINC { dup 0 eq { pop 1 } { dup SIN exch div } ifelse } bind def

/GAUSS {dup mul 2 mul dup 4 -2 roll sub dup mul exch div neg EXP exch PI mul sqrt div} bind def
%
/GAMMA { 2 dict begin				% hv 2007-08-30
  /z exch def
  1.000000000190015				% p(0)
  0 1 5 {					% on stack is 0 1 2 3 4 5 
    dup 					% n-1 n-1
    [ 76.18009172947146 
     -86.50532032941677 
      24.0140982483091 
      -1.231739572450155
       0.1208650973866179E-2 
      -0.5395239384953E-5      ] exch get exch 	% p(n) n-1
      1 add z add div			     	% p(n)/(z+n)
      add					% build the sum
    } for
    Pi 2 mul sqrt z div mul
    z 5.5 add z 0.5 add exp mul ENeperian z 5.5 add neg exp mul 
  end } bind def
%    
/GAMMALN {dup dup dup 5.5 add dup ln 3 -1 roll .5 add mul sub neg 1.000000000190015
    0 1 5 {
    [76.18009172947146 -86.50532032941677 24.0140982483091 -1.231739572450155
    .1208650973866179E-2 -.5395239384953E-5 2.5066282746310005] exch get
    4 -1 roll 1 add dup 5 1 roll div add} for
    4 -1 roll div 2.5066282746310005 mul ln add exch pop} bind def
/BETA {2 copy add GAMMALN neg exch GAMMALN 3 -1 roll GAMMALN EXP} bind def
%
/HORNER {aload length
    dup 2 add -1 roll
    exch 1 sub {
        dup 4 1 roll
        mul add exch
    } repeat
    pop
} bind def
%
/BESSEL_J0 {dup abs 8 lt {
    dup mul dup [57568490574 -13362590354 651619640.7 -11214424.18 77392.33017 -184.9052456] HORNER
    exch [57568490411 1029532985 9494680.718 59272.64853 267.8532712 1] HORNER
    Div}
    {abs dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup 
    [1 -1.098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
    3 index COS mul
    exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
    4 -1 roll SIN mul 3 -1 roll mul neg add mul} 
    ifelse} bind def
%
/BESSEL_Y0 {dup 8 lt {
    dup dup mul dup [-2957821389 7062834065 -512359803.6 10879881.29 -86327.92757 228.4622733] HORNER
    exch [40076544269 745249964.8 7189466.438 47447.26470 226.1030244 1] HORNER
    Div exch dup ln exch BESSEL_J0 .636619772 mul mul add}
    {dup .636619772 exch div sqrt exch dup .785398164 sub exch 8 exch div dup dup mul dup 
    [1 -.1098628627E-2 .2734510407E-4 -.2073370639E-5 .2093887211E-6] HORNER
    3 index SIN mul
    exch [-.1562499995E-1 .1430488765E-3 -.6911147651E-5 .7621095161E-6 -.934945152E-7] HORNER
    4 -1 roll COS mul 3 -1 roll mul add mul} 
    ifelse} bind def
%
/BESSEL_J1 {dup abs 8 lt {
    dup dup mul dup 3 -2 roll [72362614232 -7895059235 242396853.1 -2972611.439 15704.48260 -30.16036606] HORNER mul
    exch [144725228442 2300535178 18583304.74 99447.43394 376.9991397 1] HORNER
    Div}
    {dup abs dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup 
    [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
    3 index COS mul
    exch [.04687499995 6.2002690873E-3 .8449199096E-5 -.88228987E-6 .105787412E-6] HORNER
    4 -1 roll SIN mul 3 -1 roll mul neg add mul exch dup abs Div mul} 
    ifelse} bind def
%
/BESSEL_Y1 {dup 8 lt {
    dup dup dup mul dup [-.4900604943E13 .1275274390E13 -.5153428139E11 .7349264551E9 -.4237922726E7 .8511937935E4] HORNER
    exch [.2499580570E14 .4244419664E12 .3733650367E10 .2245904002E8 .1020426050E6 .3549632885E3 1] HORNER
    Div mul exch dup dup ln exch BESSEL_J1 mul exch 1 exch div sub .636619772 mul add}
    {dup .636619772 exch div sqrt exch dup 2.356194491 sub exch 8 exch div dup dup mul dup 
    [1 .183105E-2 -.3516396496E-4 .2457520174E-5 -.240337019E-6] HORNER
    3 index SIN mul
    exch [.04687499995 -.2002690873E-3 .8449199096E-5 6.88228987E-6 .105787412E-6] HORNER
    4 -1 roll COS mul 3 -1 roll mul add mul} 
    ifelse} bind def
%
% En cours...
/BESSEL_Yn {dup 0 eq {pop BESSEL_Y0}{dup 1 eq {pop BESSEL_Y1}{
    exch dup BESSEL_Y0 exch dup BESSEL_Y1 exch 2 exch Div {
        mul 3 -1 roll mul 2 index sub pstack} for
    } ifelse } ifelse } bind def
%
/SIMPSON { 1 dict begin  %% on stack a b var f ierr  Dominik Rodriguez
  3 index 5 index sub                                % compute h
  1                                                  % a b var f ierr h n
  4 index 7 index def 3 index exec                   % a b var f ierr h n f(a)
  5 index 7 index def 4 index exec add               % a b var f ierr h n f(a)+f(b)
  5 index 8 index 4 index 2 div add def 4 index exec % a b var f ierr h n f(a)+f(b) f(a+h/2)
  exch 1 index 4 mul add 0  % a b var f ierr h n old=f(a+h/2) Estim=f(a)+f(b)+4f(a+h/2) NbLoop
    {                                                % a b var f ierr h n old Estim NbLoop
      5 -1 roll 2 div dup 6 1 roll              % h<-h/2
      5 -1 roll 2 mul 5 1 roll                  % n<-2n
                                                % a b var f ierr h n old Estim NbLoop h
      2 div 10 index add 0                      % a b var f ierr h n old Estim NbLoop a+h/2 Cumul
      5 index { 
        1 index 10 index exch def 8 index exec add exch 6 index add exch 
      } repeat                                  % a b var f ierr h n old Estim NbLoop a+nh/2 Cumul
      exch pop                                  % a b var f ierr h n old Estim NbLoop New
      2 index 1 index 4 mul 6 -1 roll 2 mul sub sub % a b var f ierr h n Estim NbLoop New Diff
      4 -1 roll 2 mul 1 index sub 4 1 roll          % a b var f ierr h n Estim NbLoop New Diff
      exch 4 1 roll                             % a b var f ierr h n old Estim NbLoop Diff
      5 index 6 div mul abs 6 index lt { exit } if
      1 add dup 9 eq { exit } if
  } loop                                        % a b var f ierr h n old Estim NbLoop
  exch 5 -1 roll 6 div mul mark 10 2 roll cleartomark
end 
} def
% ------------------------------------ math stuff ----------------------------------
%
% Matrix A in arrays of rows A[[row1][row2]...]
% with [row1]=[a11 a12 ... b1]
% returns on stack solution vector X=[x1 x2 ... xn]
/SolveLinEqSystem { 				% on stack matrix M=[A,b] (A*x=b)
  10 dict begin					% hold all ocal
    /A exch def
    /Rows A length def         			% Rows = number of rows
    /Cols A 0 get length def   			% Cols = number of columns
    /Index [ 0 1 Rows 1 sub { } for ] def	% Index = [0 1 2 ... Rows-1]
    /col 0 def
    /row  0 def
    /PR Rows array def 				% PR[c] = pivot row for row row
  { 						% starts the loop, find pivot entry in row r
    col Cols ge row  Rows ge or { exit } if	% col < Cols and row < Rows else exit
    /pRow row def  				% pRow = pivot row		
    /max A row  get col get abs def		% get A[row[col]], first A[0,0] 
    row 1 add 1 Rows 1 sub { 			% starts for loop 1 1 Rows-1
      /j exch def				% index counter
      /x A j get col get abs def		% get A[j[r]]
      x max gt {				% x>max, then save position
        /pRow j def
        /max x def
      } if
    } for					% now we have the row with biggest A[0,1]
						% with pRow = the pivot row
    max 0 gt {					% swap entries pRow and row  in i 
      /tmp Index row  get def
      Index row  Index pRow get put
      Index pRow tmp put			% and columns pRow and row  in A
      /tmp A row get def
      A row  A pRow get put
      A pRow tmp put   				% pivot
      /row0  A row  get def 			% the pivoting row
      /p0 row0  col get def 			% the pivot value
      row 1 add 1 Rows 1 sub { 			% start for loop
        /j exch def
        /c1 A j get def
        /p c1 col get p0 div def
        c1 col p put				% subtract (p1/p0)*row[i] from row[j]
        col 1 add 1 Cols 1 sub {		% start for loop
          /i exch def
          c1 dup i exch 			% c1 i c1
          i get row0 i get p mul sub put
        } for
      } for
      PR row col put
      /col col 1 add def
      /row row 1 add def
    }{						% all zero entries
      /row row 1 add def			% continue loop with same row
    } ifelse
  } loop
  /X A def					% solution vector
  A Rows 1 sub get dup
  Cols 1 sub get exch
  Cols 2 sub get div
  X Rows 1 sub 3 -1 roll put  			% X[n]
  Rows 2 sub -1 0 {				% for loop to calculate X[i]
    /xi exch def				% current index
    A xi get 					% i-th row
    /Axi exch def
    /sum 0 def
    Cols 2 sub -1 xi 1 add { 
      /n exch def
      /sum sum Axi n get X n get mul add def 
    } for
    Axi Cols 1 sub get 				% b=Axi[Cols-1]
    sum sub 					% b-sum
    Axi xi get div				% b-sum / Axi[xi]
    X xi 3 -1 roll put  			% X[xi]
  } for
  X
  end 
} def
%
/c@_0 2.515517 def 
/c@_1 0.802853 def 
/c@_2 0.010328 def 
/d@_1 1.432788 def 
/d@_2 0.189269 def 
/d@_3 0.001308 def 
/norminv {
  5 dict begin
  neg 1 add 1 exch div ln 2 mul sqrt 
  /t exch def 
  /t2 t dup mul def 
  /t3 t2 t mul def 
  c@_0 c@_1 t mul add c@_2 t2 mul add 1 d@_1 t mul add 
  d@_2 t2 mul add d@_3 t3 mul add div neg t add 
  end
} def 
%end{norminv Michael Sharpe}
%
%
% END pst-math.pro

%%EndProcSet
%%BeginProcSet: pstricks-add.pro 0 0
%% $Id: pstricks-add.pro 37 2014-07-22 13:52:12Z herbert $
%%
% PostScript prologue for pstricks-add.tex.
%
% Version 0.23, 2009/12/17 
%
/tx@addDict 410 dict def tx@addDict begin
%%
realtime srand % set random generator
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/GTriangle {
  gsave
  /mtrx CM def
  /colorA ED /colorB ED /colorC ED 	% save the colors
  /yA ED /xA ED               		% save the origin
  xA yA translate
  rotate       		        	% \psk@gangle
  /yB ED /xB ED /yC ED /xC ED   	% save other coordinates
  /ds [                % save data in a array
     0 0 0 colorA aload pop     	% fd x y xr xg xb
     0 xB xA sub yB yA sub colorB aload pop
     0 xC xA sub yC yA sub colorC aload pop
%     1 xC xB add yB colorA aload pop  	% for use with 4 points ABCD
  ] def
  newpath
  <<
  /ShadingType 4           % single Gouraud
  /ColorSpace [ /DeviceRGB ]
  /DataSource ds
  >> 
  shfill
  closepath
  mtrx
  setmatrix grestore} def
%
/RGBtoCMYK {    % on stack r g b -> C M Y K
  3 dict begin
  /Blue ED /Green ED /Red ED
  1 Red sub     % Cyan
  1 Green sub   % Magenta
  1 Blue sub    % Yellow
  0   		% Black  
  end
} def
%
/CMYKtoGRAY { % on stack c m y k -> gray
  exch 0.11 mul add
  exch 0.59 mul add
  exch 0.3 mul add
  dup 1 gt { pop 1 }  if 
  neg 1 add 
} def
%
/RGBtoGRAY { % on stack r g b -> gray
  0.11 mul
  exch 0.59 mul add
  exch 0.3 mul add 
} def
%
/HSBtoGRAY { 
  6 dict begin
  /b exch def 
  /s exch def 6 mul dup cvi dup 
  /i exch def sub 
  /f exch def
  /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def
  F i get { s mul neg 1 add b mul} forall
  0.11 mul
  exch 0.59 mul add
  exch 0.3 mul add 
  end
} def
%
%% convertisseur longueur d'onde ->R,G,B       Manuel Luque
%% lambda max=780 nanometres
%% lambda min=380 nanometres
%% adaptation de :
%% http://www.physics.sfasu.edu/astro/color.html
%% www.efg2.com/lab
%
/Gamma 0.8 def
/calculateRGB {
  lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if
  lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if
  lambda 380 ge {lambda 439 le {
    /R {lambda 440 sub neg 440 380 sub div} def
    /Red R factor mul Gamma exp def
    /G 0 def
    /Green G factor mul Gamma exp def
    /B 1 def
    /Blue B factor mul Gamma exp def} if
  } if
  lambda 440 ge { lambda 489 le {
    /G {lambda 440 sub 490 440 sub div} def
    /Green G factor mul Gamma exp def
    /R 0 def /Red 0 def
    /B 1 def
    /Blue B factor mul Gamma exp def } if
  } if
  lambda 490 ge {lambda 509 le {
    /B {lambda 510 sub neg 510 490 sub div} def
    /Blue B factor mul Gamma exp def
    /R 0 def /Red 0 def
    /G 1 def
    /Green G factor mul Gamma exp def } if
  } if
  lambda 510 ge {lambda 579 le {
    /R {lambda 510 sub 580 510 sub div } def
    /Red R factor mul Gamma exp def
    /Blue 0 def
    /G 1 def
    /Green G factor mul Gamma exp def } if
  } if
  lambda 580 ge {lambda 644 le {
    /G {lambda 645 sub neg 645 580 sub div } def
    /Green G factor mul Gamma exp def
    /Blue 0 def
    /R 1 def
    /Red R factor mul Gamma exp def } if
  } if
  lambda 645 ge { lambda 780 le {
    /Red 1 factor mul Gamma exp def
    /Blue 0 def
    /Green 0 def } if
  } if
} def
%
/factor {
  lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if
  lambda 420 ge {lambda 700 le { 1 } if } if
  lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if
} def
%
/wavelengthToRGB { % the wavelength in nm must be on top of the stack
  cvi /lambda exch def % no floating point here
  calculateRGB
} def %  now the colors are saved in Red Green Blue
%
/wavelengthToGRAY { % the wavelength in nm must be on top of the stack
  cvi /lambda exch def % no floating point here
  calculateRGB
  Red Green Blue RGBtoGRAY
} def %  now the gray color is on the stack
%
/wavelengthToCMYK { % the wavelength in nm must be on top of the stack
  cvi /lambda exch def % no floating point here
  gsave
  calculateRGB Red Green Blue RGBtoCMYK 
  /Black ED /Yellow ED /Magenta ED /Cyan ED
  grestore
} def %  now the colors are saved in Cyan Magenta Yellow Black
%
/axfill {
    8 dict begin
    /xw exch def /nl exch def
    /C1 exch def /y1 exch def/x1 exch def
    /C0 exch def /y0 exch def/x0 exch def
    <<  /ShadingType 2
        /ColorSpace /DeviceRGB
        /Coords [ x0 y0 x1 y1 ]
        /EmulatorHints [ xw 2 div dup ]
        /Function <<
            /FunctionType 2
            /Domain [0 1]
            /C0 C0
            /C1 C1
            /N      1
        >>
    >> shfill
    end
} bind def
%
%/amplHand {.8} def 
%/dtHand 2 def
/varHand { rand sin amplHand mul add } def
/MovetoByHand { moveto } def 
%/MovetoByHand { /y0 ED /x0 ED x0 y0 moveto } def 
/LinetoByHand { 4 dict begin
  /y1 ED /x1 ED 
  currentpoint /y0 ED /x0 ED
  x0 x1 sub dup mul y0 y1 sub dup mul add sqrt /dEnd ED
  0 dtHand dEnd { dup
    x1 x0 sub mul dEnd div x0 add varHand exch  
    y1 y0 sub mul dEnd div y0 add varHand lineto
  } for
%  /x0 x1 def /y0 y1 def
  end
} def  
%
end
%
% END pstricks-add.pro

%%EndProcSet
%%BeginProcSet: l3backend-dvips.pro 0 0
%%
%% This is file `l3backend-dvips.pro',
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%%
%% The original source files were:
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%% l3backend-header.dtx  (with options: `header,dvips')
%% 
%% Copyright (C) 1990-2021 The LaTeX Project
%% 
%% It may be distributed and/or modified under the conditions of
%% the LaTeX Project Public License (LPPL), either version 1.3c of
%% this license or (at your option) any later version.  The latest
%% version of this license is in the file:
%% 
%%    https://www.latex-project.org/lppl.txt
%% 
%% This file is part of the "l3backend bundle" (The Work in LPPL)
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%% 
%% File: l3backend-header.dtx
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true setglobal
/pdf.globaldict 4 dict def
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/pdf.pt.dvi { 72.27 div Resolution mul } def
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/pdf.linkdp.pad { 0 } def
/pdf.linkht.pad { 0 } def
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{
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      true setglobal
      pdf.globaldict
        /pdf.brokenlink.rect [ pdf.outerbox aload pop ] put
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      pdf.globaldict
        /pdf.brokenlink.dict
          pdf.link.dict pdf.cvs put
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      mark pdf.link.dict cvx exec /Rect
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          pdf.llx
          pdf.lly
          pdf.outerbox 2 get pdf.linkmargin add
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      /ANN pdf.pdfmark
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}
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/pdf.bordertracking.continue
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    /pdf.link.dict pdf.globaldict
      /pdf.brokenlink.dict get def
    /pdf.outerbox pdf.globaldict
      /pdf.brokenlink.rect get def
    /pdf.baselineskip pdf.globaldict
      /pdf.brokenlink.skip get def
    pdf.globaldict dup dup
    /pdf.brokenlink.dict undef
    /pdf.brokenlink.skip undef
    /pdf.brokenlink.rect undef
    currentpoint
    /pdf.originy exch def
    /pdf.originx exch def
    /a where
      {
        /a
          {
            moveto
            SDict
            begin
            currentpoint pdf.originy ne exch
              pdf.originx ne or
              {
                pdf.save.linkll
                /pdf.lly
                  pdf.lly pdf.outerbox 1 get sub def
                pdf.bordertracking.begin
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            if
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        put
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    /x where
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            0 exch rmoveto
            SDict
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            pdf.originy ne exch pdf.originx ne or
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                pdf.save.linkll
                /pdf.lly
                  pdf.lly pdf.outerbox 1 get sub def
                pdf.bordertracking.begin
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            if
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          }
        put
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    if
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/pdf.breaklink
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    pop
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          {
           pdf.count 0 eq { exit } if
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                 pdf.linkmargin 2 mul add sub
                 3 exch put
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                 pdf.outerbox 2 get
                 pdf.linkmargin add
                 2 exch put
               dup dup
                 3 get
                 pdf.outerbox pdf.rect.ht
                 pdf.linkmargin 2 mul add add
                 1 exch put
               /pdf.currentrect exch  def
               pdf.breaklink.write
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                   pdf.currentrect
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                     pdf.outerbox 0 get
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                     0 exch put
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                     pdf.outerbox 2 get
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                   dup dup
                     1 get
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                     1 exch put
                   dup dup
                     3 get
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                1 index 3 get
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                pdf.baselineskip div round cvi 1 sub
                exch
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              dup
                pdf.outerbox 0 get
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              dup dup
                1 get
                pdf.baselineskip add
                1 exch put
              dup dup
                3 get
                pdf.baselineskip add
                3 exch put
              dup 2 index 2 get  2 exch put
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              pdf.breaklink.write
              SDict /pdf.pdfmark.good false put
              exit
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            { pdf.count 2 sub /pdf.count exch def }
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/pdf.pdfmark
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        SDict /pdf.outerbox undef
        SDict /pdf.baselineskip undef
        currentdict /pdf.pdfmark.dict undef
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          {
            pdf.pdfmark.dict
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    loop
}
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%% 
%%
%% End of file `l3backend-dvips.pro'.

%%EndProcSet
%%BeginProcSet: 8r.enc 0 0
% File 8r.enc  TeX Base 1 Encoding  Revision 2.0  2002-10-30
%
% @@psencodingfile@{
%   author    = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry,
%                W. Schmidt, P. Lehman",
%   version   = "2.0",
%   date      = "27nov06",
%   filename  = "8r.enc",
%   email     = "tex-fonts@@tug.org",
%   docstring = "This is the encoding vector for Type1 and TrueType
%                fonts to be used with TeX.  This file is part of the
%                PSNFSS bundle, version 9"
% @}
% 
% The idea is to have all the characters normally included in Type 1 fonts
% available for typesetting. This is effectively the characters in Adobe
% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol,
% MacRoman, and some extra characters from Lucida.
% 
% Character code assignments were made as follows:
% 
% (1) the Windows ANSI characters are almost all in their Windows ANSI
% positions, because some Windows users cannot easily reencode the
% fonts, and it makes no difference on other systems. The only Windows
% ANSI characters not available are those that make no sense for
% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
% (173). quotesingle and grave are moved just because it's such an
% irritation not having them in TeX positions.
% 
% (2) Remaining characters are assigned arbitrarily to the lower part
% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
% 
% (3) Y&Y Lucida Bright includes some extra text characters; in the
% hopes that other PostScript fonts, perhaps created for public
% consumption, will include them, they are included starting at 0x12.
% These are /dotlessj /ff /ffi /ffl.
% 
% (4) hyphen appears twice for compatibility with both ASCII and Windows.
%
% (5) /Euro was assigned to 128, as in Windows ANSI
%
% (6) Missing characters from MacRoman encoding incorporated as follows:
%
%     PostScript      MacRoman        TeXBase1
%     --------------  --------------  --------------
%     /notequal       173             0x16
%     /infinity       176             0x17
%     /lessequal      178             0x18
%     /greaterequal   179             0x19
%     /partialdiff    182             0x1A
%     /summation      183             0x1B
%     /product        184             0x1C
%     /pi             185             0x1D
%     /integral       186             0x81
%     /Omega          189             0x8D
%     /radical        195             0x8E
%     /approxequal    197             0x8F
%     /Delta          198             0x9D
%     /lozenge        215             0x9E
%
/TeXBase1Encoding [
% 0x00
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 /fraction /hungarumlaut /Lslash /lslash
 /ogonek /ring /.notdef /breve
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% 0x10
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 /product /pi /grave /quotesingle
% 0x20
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 /parenleft /parenright /asterisk /plus
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% 0x30
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 /less /equal /greater /question
% 0x40
 /at /A /B /C
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% 0x50
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% 0x70
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% 0x80
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 /quotedblbase /ellipsis /dagger /daggerdbl
 /circumflex /perthousand /Scaron /guilsinglleft
 /OE /Omega /radical /approxequal
% 0x90
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% 0xA0
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 /dieresis /copyright /ordfeminine /guillemotleft
 /logicalnot /hyphen /registered /macron
% 0xB0
 /degree /plusminus /twosuperior /threesuperior
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 /cedilla /onesuperior /ordmasculine /guillemotright
 /onequarter /onehalf /threequarters /questiondown
% 0xC0
 /Agrave /Aacute /Acircumflex /Atilde
 /Adieresis /Aring /AE /Ccedilla
 /Egrave /Eacute /Ecircumflex /Edieresis
 /Igrave /Iacute /Icircumflex /Idieresis
% 0xD0
 /Eth /Ntilde /Ograve /Oacute
 /Ocircumflex /Otilde /Odieresis /multiply
 /Oslash /Ugrave /Uacute /Ucircumflex
 /Udieresis /Yacute /Thorn /germandbls
% 0xE0
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 /adieresis /aring /ae /ccedilla
 /egrave /eacute /ecircumflex /edieresis
 /igrave /iacute /icircumflex /idieresis
% 0xF0
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 /oslash /ugrave /uacute /ucircumflex
 /udieresis /yacute /thorn /ydieresis
] def


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setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90
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0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{
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setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0
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DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70
setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0
setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1
setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end

%%EndProcSet
TeXDict begin @defspecial

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pgfstartx 10 index pgfdiffx pgfdomb div mul add def /pgfcircye pgfstarty
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sub pgfdiff div def /pgfystep pgfcircye pgfcircy sub pgfdiff div def
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8 index sub pgfdiff div 3 index 8 index sub pgfdiff div 11 index 11
index 11 index 11 index 17 index pgfdiff { 4 index 4 index 4 index
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def

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def /.setblendmode where {pop} {/.setblendmode{pop}def} ifelse /.setfillconstantalpha
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1 def /.pushpdf14devicefilter where {pop [userdict /bop-hook known
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put pop pop pop } bind def /pgfwritesamplegray { pgfcheckcolorrange
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} bind def /pgfcheckcolorrange { dup 0.0 lt {pop 0.0} if dup 1.0 gt
{pop 1.0} if } bind def /pgfchanneldepthcmyk 8 def /pgfchanneldepthrgb
8 def /pgfchanneldepthgray 24 def /pgfcolorsamplecmyk 4 string def
/pgfcolorsamplergb 3 string def /pgfcolorsamplegray 3 string def /pgfrangecmyk
[0 1 0 1 0 1 0 1] def /pgfrangergb [0 1 0 1 0 1] def /pgfrangegray
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def

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@fedspecial end
%%BeginFont: URWPalladioL-BoldItal
%!PS-AdobeFont-1.0: URWPalladioL-BoldItal 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (URW Palladio L Bold Italic) readonly def
/FamilyName (URW Palladio L) readonly def
/Weight (Bold) readonly def
/ItalicAngle -9.9 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /URWPalladioL-BoldItal def
/PaintType 0 def
/WMode 0 def
/FontBBox {-170 -300 1073 935} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: rsfs10
%!PS-AdobeFont-1.0: rsfs10 001.000
%%CreationDate: Sat Mar 21 18:47:14 1998
%%VMusage: 120000 150000
11 dict begin
/FontInfo 14 dict dup begin
/version (001.001) readonly def
/Copyright (Conversion from mf curves by Metafog (c) 1995 Richard Kinch) readonly def
/Notice (Copyright (c) Taco Hoekwater, 1998. All rights reserved.) readonly def
/FullName (rsfs10) readonly def
/FamilyName (rsfs10) readonly def
/ItalicAngle -12 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Weight (Roman) readonly def
end readonly def
/FontName /rsfs10 def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 67 /C put
readonly def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox {-2 -300 1240 728} readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: Pxsyb
%!PS-AdobeFont-1.0: Pxsyb 1.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 28851
20 dict begin
/FontInfo 16 dict dup begin
/version (1.0) readonly def
/FullName (Pxsyb) readonly def
/FamilyName (Pxsyb) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 1.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /Pxsyb def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 49 /notforces put
dup 50 /notsatisfies put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-47 -197 2356 836}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: URWPalladioL-Ital
%!PS-AdobeFont-1.0: URWPalladioL-Ital 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (URW Palladio L Italic) readonly def
/FamilyName (URW Palladio L) readonly def
/Weight (Regular) readonly def
/ItalicAngle -9.5 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /URWPalladioL-Ital def
/PaintType 0 def
/WMode 0 def
/FontBBox {-170 -305 1010 941} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: Rpxmi
%!PS-AdobeFont-1.0: Rpxmi 1.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 19695
20 dict begin
/FontInfo 16 dict dup begin
/version (1.0) readonly def
/FullName (Rpxmi) readonly def
/FamilyName (Rpxmi) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 1.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /Rpxmi def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /Gamma put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-70 -289 949 802}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: URWPalladioL-Roma
%!PS-AdobeFont-1.0: URWPalladioL-Roma 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (URW Palladio L Roman) readonly def
/FamilyName (URW Palladio L) readonly def
/Weight (Roman) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /URWPalladioL-Roma def
/PaintType 0 def
/WMode 0 def
/FontBBox {-166 -283 1021 943} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: Pxsy
%!PS-AdobeFont-1.0: Pxsy 1.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 24558
20 dict begin
/FontInfo 16 dict dup begin
/version (1.0) readonly def
/FullName (Pxsy) readonly def
/FamilyName (Pxsy) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 1.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /Pxsy def
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dup 17 /equivalence put
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dup 44 /arrowdblboth put
dup 48 /prime put
dup 50 /element put
dup 56 /universal put
dup 57 /existential put
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dup 86 /V put
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dup 95 /logicalor put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 110 /backslash put
dup 125 /diamond put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-21 -994 1292 912}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: Pxsyc
%!PS-AdobeFont-1.0: Pxsyc 1.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 31504
20 dict begin
/FontInfo 16 dict dup begin
/version (1.0) readonly def
/FullName (Pxsyc) readonly def
/FamilyName (Pxsyc) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 1.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /Pxsyc def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 44 /nequal put
dup 46 /nequivalence put
dup 60 /nelement put
dup 74 /strict put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-179 -347 1406 887}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: URWPalladioL-Bold
%!PS-AdobeFont-1.0: URWPalladioL-Bold 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (URW Palladio L Bold) readonly def
/FamilyName (URW Palladio L) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /URWPalladioL-Bold def
/PaintType 0 def
/WMode 0 def
/FontBBox {-152 -301 1000 935} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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4 v 863 1163 4 200 v 916 1033 a Ft(fracamente)c(densa:)916
1133 y Fm(8)p Fo(u)p Fm(8)p Fo(v)p Ft(\()p Fo(Ruv)k Fm(!)g(9)p
Fo(w)p Ft(\()p Fo(Ruw)c Fm(^)g Fo(Rwv)p Ft(\))p 2147
1163 V 2200 1033 a Fn(\003\003)p Fo(p)j Fm(!)h Fn(\003)p
Fo(p)p 3476 1163 V 863 1166 2617 4 v 863 1465 4 299 v
916 1236 a Ft(fracamente)c(conectada:)916 1336 y Fm(8)p
Fo(w)p Fm(8)p Fo(u)p Fm(8)p Fo(v)p Ft(\()p Fo(Rwu)g Fm(^)g
Fo(Rwv)k Fm(!)916 1435 y Fo(Ruv)c Fm(_)f Fo(u)23 b Fs(=)g
Fo(v)18 b Fm(_)g Fo(Rvu)p Ft(\))p 2147 1465 V 2200 1236
a Fn(\003)p Ft(\(\()p Fo(p)f Fm(^)h Fn(\003)p Fo(p)p
Ft(\))k Fm(!)h Fo(q)p Ft(\))c Fm(_)g Fn(\003)p Ft(\(\()p
Fo(q)e Fm(^)i Fn(\003)p Fo(q)p Ft(\))k Fm(!)g Fo(p)p
Ft(\))p 3476 1465 V 863 1468 2617 4 v 863 1767 4 299
v 916 1538 a(fracamente)c(dir)o(ecionada:)916 1638 y
Fm(8)p Fo(w)p Fm(8)p Fo(u)p Fm(8)p Fo(v)p Ft(\()p Fo(Rwu)g
Fm(^)g Fo(Rwv)k Fm(!)916 1737 y(9)p Fo(t)p Ft(\()p Fo(Rut)18
b Fm(^)h Fo(Rvt)p Ft(\)\))p 2147 1767 V 2200 1538 a Fm(})p
Fn(\003)p Fo(p)k Fm(!)g Fn(\003)p Fm(})p Fo(p)p 3476
1767 V 863 1771 2617 4 v 1302 1888 a Ft(T)-8 b(abela)20
b(2.2:)p 0 TeXcolorgray 1713 1888 a
SDict begin H.S end
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1888 a
SDict begin H.R end
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SDict begin [/View [/XYZ H.V]/Dest (table.2.2) cvn /DEST pdfmark end
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Ft(Mais)g(cinco)h(fatos)g(de)f(corr)o(espond\352ncia)p
0 0 0 TeXcolorrgb 756 2210 a(r)o(ela\347\343o)j(de)i(acessibilidade)f
Fo(R)i Ft(\351)f(par)o(cialmente)f(funcional,)j(se)e(a)g(partir)f(de)h
(qualquer)756 2335 y(mundo)17 b(no)g(m\341ximo)g(um)f(mundo)i(\351)e
(acess\355vel.)26 b(Se)16 b(\351)g(o)h(caso)f(que)h(de)f(qualquer)h
(mundo)756 2459 y(exatamente)h(um)i(mundo)g(\351)f(acess\355vel,)f
(chamamo-la)h(funcional.)29 b(\(Assim)20 b(as)f(r)o(ela\347\365es)756
2584 y(funcionais)k(s\343o)f(pr)o(ecisamente)g(aquelas)g(que)h(s\343o)f
(tanto)h(seriais)g(como)g(par)o(cialmente)756 2708 y(funcionais\).)28
b(Elas)20 b(s\343o)f(chamadas)g(funcionais,)h(por)o(que)g(a)f(r)o
(ela\347\343o)f(de)i(acessibilidade)756 2833 y(opera)f(como)i(uma)g
(fun\347\343o)f(\(par)o(cial\).)26 b(Uma)20 b(r)o(ela\347\343o)f(\351)h
(fracamente)f(densa)h(se)g(sempr)o(e)756 2957 y(que)h
Fo(Ruv)p Ft(,)f(existe)h(um)g Fo(w)g Ft(\223entr)o(e\224)d
Fo(u)j Ft(e)g Fo(v)p Ft(.)p 0 0 0 TeXcolorrgb 0 0 0 TeXcolorrgb
eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF
